EBK CALCULUS EARLY TRANSCENDENTALS SING
11th Edition
ISBN: 8220102011618
Author: Davis
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 13.4, Problem 56ES
The speed of sound
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Lake Ontario has a volume of approximately V =1600 km3. It is heavily polluted by a certain pollutant with a concentration of co = 0.1%.As a part pollution control, the pollutant concentration of the inflow is reduced to cin = 0.02%. The inflow and outflow rates Qin = Qout = Q = 500 km3 per year. Suppose that pollutant from the inflow is well mixed with the lake water before leaving the lake. How long will it take for the pollutant concentration in the lake to reduce to 0.05%?
The flow rate of a pipe, Q in (m/s) is given by Q =
dV
where V is
dt
volume (in m) and t is time in (s). The volume in a pipe at time t is
given in Table 1.
Table 1
4 6
t, s
2
8
10
V(t), m3
7.56
3.87
5.09
6.34
4.59
Estimate the flow rate Q at time t = 4s by using:
(a)
2-Point Forward Difference
(b)
2-Point Backward Difference
(c)
3-Point Central Difference
The sides of a cube box without lid are measured to be 4 cm, with a possible error
of 0.2cm
If A is the surface area, and s is the side length. Interpret the differential
dA in terms of ds first.
Your answer
Estimate the possible propagated error in the calculated surface area. *
Your answer
What's the related error? *
Your answer
If V is the volume, and s is the side length. Interpret the differential dV in
terms of ds first.
Your answer
Estimate the possible propagated error in the calculated volume *
Chapter 13 Solutions
EBK CALCULUS EARLY TRANSCENDENTALS SING
Ch. 13.1 - Prob. 1QCECh. 13.1 - Let f(x,y)=xyx+y+1....Ch. 13.1 - Let f(x,y)=ex+y. (a) For what values of k will the...Ch. 13.1 - Let f(x,y,z)=1x2+y2+z2+1. (a) For what values of k...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...
Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - Suppose that the concentration C in mg/L of...Ch. 13.1 - Suppose that the concentration C in mg/L of...Ch. 13.1 - Refer to Table 13.1.1 to estimate the given...Ch. 13.1 - Refer to Table 13.1.1 to estimate the given...Ch. 13.1 - Refer to Table 13.1.1 to estimate the given...Ch. 13.1 - Refer to Table 13.1.1 to estimate the given...Ch. 13.1 - One method for determining relative humidity is to...Ch. 13.1 - Use the table in Exercise 15 to complete parts...Ch. 13.1 - These exercises involve functions of three...Ch. 13.1 - These exercises involve functions of three...Ch. 13.1 - These exercises involve functions of three...Ch. 13.1 - These exercises involve functions of three...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - These exercises are concerned with functions of...Ch. 13.1 - Prob. 23ESCh. 13.1 - Sketch the domain of f. Use solid lines for...Ch. 13.1 - Sketch the domain of f. Use solid lines for...Ch. 13.1 - Sketch the domain of f. Use solid lines for...Ch. 13.1 - Describe the domain of f in words....Ch. 13.1 - Describe the domain of f in words....Ch. 13.1 - Prob. 29ESCh. 13.1 - Determine whether the statement is true or false....Ch. 13.1 - Determine whether the statement is true or false....Ch. 13.1 - Determine whether the statement is true or false....Ch. 13.1 - Sketch the graph of f. f(x,y)=3Ch. 13.1 - Sketch the graph of f. f(x,y)=9x2y2Ch. 13.1 - Sketch the graph of f. f(x,y)=x2+y2Ch. 13.1 - Sketch the graph of f. f(x,y)=x2+y2Ch. 13.1 - Sketch the graph of f. f(x,y)=x2y2Ch. 13.1 - Sketch the graph of f. f(x,y)=4x2y2Ch. 13.1 - Sketch the graph of f. f(x,y)=x2+y2+1Ch. 13.1 - Sketch the graph of f. f(x,y)=x2+y21Ch. 13.1 - Sketch the graph of f. f(x,y)=y+1Ch. 13.1 - Sketch the graph of f. f(x,y)=x2Ch. 13.1 - In each part, select the term that best describes...Ch. 13.1 - In each part, select the term that best describes...Ch. 13.1 - Refer to Figure 13.1.7 in each part. Suppose that...Ch. 13.1 - Refer to Figure 13.1.7 in each part. Suppose that...Ch. 13.1 - In each part, match the contour plot with one of...Ch. 13.1 - Prob. 48ESCh. 13.1 - In each part, the questions refer to the contour...Ch. 13.1 - A curve connecting points of equal atmospheric...Ch. 13.1 - Sketch the level curve z=k for the specified...Ch. 13.1 - Sketch the level curve z=k for the specified...Ch. 13.1 - Sketch the level curve z=k for the specified...Ch. 13.1 - Sketch the level curve z=k for the specified...Ch. 13.1 - Sketch the level curve z=k for the specified...Ch. 13.1 - Sketch the level curve z=k for the specified...Ch. 13.1 - Sketch the level surface f(x,y,z)=k ....Ch. 13.1 - Sketch the level surface f(x,y,z)=k ....Ch. 13.1 - Sketch the level surface f(x,y,z)=k ....Ch. 13.1 - Sketch the level surface f(x,y,z)=k ....Ch. 13.1 - Describe the level surfaces in words....Ch. 13.1 - Describe the level surfaces in words....Ch. 13.1 - Describe the level surfaces in words....Ch. 13.1 - Describe the level surfaces in words....Ch. 13.1 - Let f(x,y)=x22x3+3xy. Find an equation of the...Ch. 13.1 - Let f(x,y)=yex. Find an equation of the level...Ch. 13.1 - Let f(x,y,z)=x2+y2z. Find an equation of the level...Ch. 13.1 - Letfx,y,z=xyz+3. Find an equation of the level...Ch. 13.1 - If Tx,y is the temperature at a point x,y on a...Ch. 13.1 - Prob. 70ESCh. 13.1 - Let fx,y=x2+y3. (a) Use a graphing utility to...Ch. 13.1 - Let f(x,y)=xe(x2+y2). (a) Use a CAS to generate...Ch. 13.1 - Let f(x,y)=110exsiny. (a) Use a CAS to generate...Ch. 13.1 - In each part. describe in words how the graph of g...Ch. 13.1 - (a) Sketch the graph of fx,y=e(x2+y2). (b)...Ch. 13.2 - Prob. 1QCECh. 13.2 - ...Ch. 13.2 - A function fx,y is continuous at x0,y0 provided...Ch. 13.2 - Determine all value of the constant a such that...Ch. 13.2 - Prob. 1ESCh. 13.2 - Prob. 2ESCh. 13.2 - Prob. 3ESCh. 13.2 - Prob. 4ESCh. 13.2 - Prob. 5ESCh. 13.2 - Prob. 6ESCh. 13.2 - Prob. 7ESCh. 13.2 - Prob. 8ESCh. 13.2 - Prob. 9ESCh. 13.2 - Prob. 10ESCh. 13.2 - Prob. 11ESCh. 13.2 - Prob. 12ESCh. 13.2 - Prob. 13ESCh. 13.2 - Prob. 14ESCh. 13.2 - Prob. 15ESCh. 13.2 - Prob. 16ESCh. 13.2 - Prob. 17ESCh. 13.2 - Prob. 18ESCh. 13.2 - Prob. 19ESCh. 13.2 - Prob. 20ESCh. 13.2 - Prob. 21ESCh. 13.2 - Prob. 22ESCh. 13.2 - Prob. 23ESCh. 13.2 - Prob. 24ESCh. 13.2 - Prob. 25ESCh. 13.2 - Prob. 26ESCh. 13.2 - Evaluate the limits by converting to spherical...Ch. 13.2 - Evaluate the limits by converting to spherical...Ch. 13.2 - Determine whether the statement is true or false....Ch. 13.2 - Determine whether the statement is true or false....Ch. 13.2 - Determine whether the statement is true or false....Ch. 13.2 - Determine whether the statement is true or false....Ch. 13.2 - The accompanying figure shows a portion of the...Ch. 13.2 - (a) Show that as x,y0,0 along any straight line...Ch. 13.2 - Prob. 35ESCh. 13.2 - Find limx,y0,1tan1x2+1x2+y12.Ch. 13.2 - Find limx,y0,1tan1x21x2+y12.Ch. 13.2 - Prob. 38ESCh. 13.2 - Prob. 39ESCh. 13.2 - Prob. 40ESCh. 13.2 - Prob. 41ESCh. 13.2 - Prob. 42ESCh. 13.2 - Prob. 43ESCh. 13.2 - Sketch the largest region on which the function f...Ch. 13.2 - Prob. 45ESCh. 13.2 - Sketch the largest region on which the function f...Ch. 13.2 - Sketch the largest region on which the function f...Ch. 13.2 - Sketch the largest region on which the function f...Ch. 13.2 - Prob. 49ESCh. 13.2 - Prob. 50ESCh. 13.2 - Prob. 51ESCh. 13.2 - Describe the largest region on which the function...Ch. 13.2 - Describe the procedure you would use to deter-mine...Ch. 13.3 - Letfx,y=xsinxy.Thenfxx,y=andfyx,y=.Ch. 13.3 - The slope of the surface z=xy2 in the x-direction...Ch. 13.3 - The volume V of a right circular cone of radius r...Ch. 13.3 - Prob. 4QCECh. 13.3 - Let fx,y=3x3y2. Find...Ch. 13.3 - Let z=e2xsiny. Find....Ch. 13.3 - Prob. 3ESCh. 13.3 - Prob. 4ESCh. 13.3 - Prob. 5ESCh. 13.3 - Prob. 6ESCh. 13.3 - Prob. 7ESCh. 13.3 - Prob. 8ESCh. 13.3 - Evaluate the indicated partial derivatives....Ch. 13.3 - Prob. 10ESCh. 13.3 - Let fx,y=3x+2y. (a) Find the slope of the surface...Ch. 13.3 - Let fx,y=xey+5y. (a) Find the slope of the surface...Ch. 13.3 - Let z=siny24x. (a) Find the rate of change of z...Ch. 13.3 - Let z=x+y1. (a) Find the rate of change of z with...Ch. 13.3 - Use the information in the accompanying figure to...Ch. 13.3 - Prob. 16ESCh. 13.3 - Prob. 17ESCh. 13.3 - Use the table in Exercise 17 and the method of...Ch. 13.3 - Prob. 19ESCh. 13.3 - What can you say about the sign of...Ch. 13.3 - Determine whether the statement is true or false....Ch. 13.3 - Determine whether the statement is true or false....Ch. 13.3 - Determine whether the statement is true or false....Ch. 13.3 - Determine whether the statement is true or false....Ch. 13.3 - Find z/xandz/y. z=4ex2y3Ch. 13.3 - Find z/xandz/y. z=cosx5y4Ch. 13.3 - Find z/xandz/y. z=x3ln1+xy3/5Ch. 13.3 - Find z/xandz/y. z=exysin4y2Ch. 13.3 - Find
Ch. 13.3 - Find z/xandz/y. z=x2y3x+yCh. 13.3 - Find fxx,yandfyx,y. fx,y=3x5y7x3yCh. 13.3 - Findfxx,yandfyx,y. fx,y=x+yxyCh. 13.3 - Find fxx,yandfyx,y. fx,y=y3/2tan1x/yCh. 13.3 - Find fxx,yandfyx,y. fx,y=x3ey+y3secxCh. 13.3 - Find fxx,yandfyx,y. fx,y=y2tanx4/3Ch. 13.3 - Find fxx,yandfyx,y. fx,y=coshxsinh2xy2Ch. 13.3 - Prob. 37ESCh. 13.3 - Prob. 38ESCh. 13.3 - Prob. 39ESCh. 13.3 - Prob. 40ESCh. 13.3 - ...Ch. 13.3 - ...Ch. 13.3 - Findfx,fyandfz.fx,y,z=zlnx2ycoszCh. 13.3 - Findfx,fyandfz. fx,y,z=y3/2secxzyCh. 13.3 - Findfx,fyandfz. fx,y,z=tan11xy2z3Ch. 13.3 - Findfx,fyandfz. fx,y,z=coshzsinh2x2yzCh. 13.3 - Prob. 47ESCh. 13.3 - Prob. 48ESCh. 13.3 - Prob. 49ESCh. 13.3 - Prob. 50ESCh. 13.3 - Letfx,y,z=y2exz.Findaf/x1,1,1bf/y1,1,1cf/z1,1,1.Ch. 13.3 - Letw=x2+4y2z2.Findaw/x2,1,1bw/y2,1,1cw/z2,1,1Ch. 13.3 - Let fx,y=excosy. Use a graphing utility to graph...Ch. 13.3 - Let fx,y=exsiny. Use a graphing utility to graph...Ch. 13.3 - A point moves along the intersection of the...Ch. 13.3 - A point moves along the intersection of the...Ch. 13.3 - A point moves along the intersection of the plane...Ch. 13.3 - Find the slope of the tangent line at 1,1,5 to the...Ch. 13.3 - The volume V of a right circular cylinder is given...Ch. 13.3 - The volume V of a right circular cone is given by...Ch. 13.3 - Prob. 61ESCh. 13.3 - Prob. 62ESCh. 13.3 - The length, width, and height of a rectangular box...Ch. 13.3 - The area A of a triangle is given by A=12absin,...Ch. 13.3 - The volume of a right circular cone of radius r...Ch. 13.3 - Find parametric equations for the tangent line at...Ch. 13.3 - (a) By differentiating implicitly, find the slope...Ch. 13.3 - (a) By differentiating implicitly, find the slope...Ch. 13.3 - Calculate z/xandz/y using implicit...Ch. 13.3 - Calculate z/xandz/y using implicit...Ch. 13.3 - Calculate z/xandz/y using implicit...Ch. 13.3 - Calculate z/xandz/y using implicit...Ch. 13.3 - Find w/x,w/y,andw/z using implicit...Ch. 13.3 - Find w/x,w/y,andw/z using implicit...Ch. 13.3 - Find w/x,w/y,andw/z using implicit...Ch. 13.3 - Find w/x,w/y,andw/z using implicit...Ch. 13.3 - Findfxandfy. fx,y=yxet2dtCh. 13.3 - Findfxandfy. fx,y=1xyet2dtCh. 13.3 - Findfxandfy. fx,y=0x2y3et2sint3dtCh. 13.3 - Findfxandfy. fx,y=x+yxysint3dtCh. 13.3 - z=xcosy.Finda2z/x2b2z/y2c2z/xyd2z/yx.Ch. 13.3 - Letfx,y=4x22y+7x4y5.Findafxxbfyycfxydfyx.Ch. 13.3 - Letfx,y=sin3x2+6y2.Findafxxbfyycfxydfyx.Ch. 13.3 - Letfx,y=xe2y.Findafxxbfyycfxydfyx.Ch. 13.3 - Prob. 85ESCh. 13.3 - Confirm that the mixed second-order derivatives of...Ch. 13.3 - Confirm that the mixed second-order derivatives of...Ch. 13.3 - Confirm that the mixed second-order derivatives of...Ch. 13.3 - Confirm that the mixed second-order derivatives of...Ch. 13.3 - Confirm that the mixed second-order derivatives of...Ch. 13.3 - Confirm that the mixed second-order derivatives of...Ch. 13.3 - Prob. 92ESCh. 13.3 - Express the following derivatives in notation....Ch. 13.3 - Express the derivatives in “subscript�...Ch. 13.3 - Given fx,y=x3y52x2y+x,find afxxybfyxycfyyy.Ch. 13.3 - Given z=2xy5,find a3zyxyb3zx2yc4zx2y2.Ch. 13.3 - Given fx,y=y3e5x,findafxxy0,1bfxxx0,1cfyyxx0,1.Ch. 13.3 - Prob. 98ESCh. 13.3 - ...Ch. 13.3 - Letw=4x3y+2z5.Finda2wxzb3wxyzc4wz2yx.Ch. 13.3 - Show that the function satisfies Laplace’s...Ch. 13.3 - Show that the function satisfies the heat equation...Ch. 13.3 - Show that the function ux,t=sinctsinx satisfies...Ch. 13.3 - In each part, show that ux,yandx,y satisfy the...Ch. 13.3 - Prob. 105ESCh. 13.3 - Prob. 106ESCh. 13.3 - Find the indicated derivatives....Ch. 13.3 - Find the indicated derivatives....Ch. 13.3 - Prob. 109ESCh. 13.3 - Find the indicated derivatives....Ch. 13.3 - Prob. 111ESCh. 13.3 - ...Ch. 13.3 - Findw/xifori=1,2,...,n. w=cosx1+2x2++nxnCh. 13.3 - Findw/xifori=1,2,...,n. w=k=1nxk1/nCh. 13.3 - Describe the largest set on which Theorem 13.3.2...Ch. 13.3 - Describe the largest set on which Theorem 13.3.2...Ch. 13.3 - Let fx,y=2x23xy+y2. Find fx2,1andfy2,1 by...Ch. 13.3 - ...Ch. 13.3 - Let fx,y=x3+y31/3. (a) Show that fy0,0=1. (b) At...Ch. 13.4 - Assume that fx,y is differentiable at x0,y0 and...Ch. 13.4 - Compute the differential of each function....Ch. 13.4 - If f is differentiable at x0,y0, then the local...Ch. 13.4 - Assume that f1,2=4 and fx,y is differentiable at...Ch. 13.4 - Prob. 1ESCh. 13.4 - Suppose that a function fx,y is differentiable at...Ch. 13.4 - Prob. 3ESCh. 13.4 - Prob. 4ESCh. 13.4 - Use Definitions 13.4.1 and 13.4.2 to prove that a...Ch. 13.4 - Use Definitions 13.4.1 and 13.4.2 to prove that a...Ch. 13.4 - Use Definition 13.4.2 to prove that...Ch. 13.4 - Use Definition 13.4.2 to determine all values of r...Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Compute the differential dzordw of the function....Ch. 13.4 - Use a total differential to approximate the change...Ch. 13.4 - Use a total differential to approximate the change...Ch. 13.4 - Use a total differential to approximate the change...Ch. 13.4 - Use a total differential to approximate the change...Ch. 13.4 - Use a total differential to approximate the change...Ch. 13.4 - Use a total differential to approximate the change...Ch. 13.4 - Determine whether the statement is true or false....Ch. 13.4 - Determine whether the statement is true or false....Ch. 13.4 - Determine whether the statement is true or false....Ch. 13.4 - Determine whether the statement is true or false....Ch. 13.4 - In the accompanying figure a rectangle with...Ch. 13.4 - The volume V of a right circular cone of radius r...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - (a) Find the local linear approximation L to the...Ch. 13.4 - In each part, confirm that the stated formula is...Ch. 13.4 - Show that the local linear approximation of the...Ch. 13.4 - In each part, confirm that the stated formula is...Ch. 13.4 - Based on Exercise 42, what would you conjecture is...Ch. 13.4 - Suppose that a function fx,y differentiable at the...Ch. 13.4 - Suppose that a function fx,y is differentiable at...Ch. 13.4 - Suppose that a function fx,y,z is differentiable...Ch. 13.4 - Suppose that a function fx,y,z is differentiable...Ch. 13.4 - A function f is given along with a local linear...Ch. 13.4 - A function f is given along with a local linear...Ch. 13.4 - Prob. 51ESCh. 13.4 - Prob. 52ESCh. 13.4 - The length and width of a rectangle are measured...Ch. 13.4 - The radius and height of a right circular cone are...Ch. 13.4 - The period T of a simple pendulum with small...Ch. 13.4 - The speed of sound in a medium of bulk modulus B...Ch. 13.4 - The magnitude E of an electric field at a point...Ch. 13.4 - According to the ideal gas law, the pressure,...Ch. 13.4 - Suppose that certain measured quantities x and y...Ch. 13.4 - The total resistance R of three resistances...Ch. 13.4 - The area of a triangle is to be computed from the...Ch. 13.4 - The length, width, and height of a rectangular box...Ch. 13.4 - Use Theorem 13.4.4 to prove that fx,y=x2siny is...Ch. 13.4 - Use Theorem 13.4.4 to prove that fx,y,z=xysinz is...Ch. 13.4 - Prob. 65ESCh. 13.4 - Prob. 66ESCh. 13.4 - Discuss the similarities and differences between...Ch. 13.5 - Suppose that z=xy2 and x and y are differentiable...Ch. 13.5 - Suppose that C is the graph of the equation fx,y=1...Ch. 13.5 - A rectangle is growing in such a way that when its...Ch. 13.5 - Prob. 4QCECh. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Use an appropriate form of the chain rule to find...Ch. 13.5 - Prob. 11ESCh. 13.5 - Prob. 12ESCh. 13.5 - Suppose that z=fx,y is differentiable at the...Ch. 13.5 - Prob. 14ESCh. 13.5 - Explain how the product rule for functions of a...Ch. 13.5 - A student attempts to differentiate the function...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use appropriate forms of the chain rule to find...Ch. 13.5 - Use a chain rule to find the value of...Ch. 13.5 - Use a chain rule to find the values of...Ch. 13.5 - Use a chia rule to find the values of...Ch. 13.5 - Use a chain rule to find...Ch. 13.5 - Let a and b denote two sides of a triangle and let...Ch. 13.5 - The voltage, V (in volts), across a circuit is...Ch. 13.5 - Determine whether the statement is true or false....Ch. 13.5 - Determine whether the statement is true or false....Ch. 13.5 - Determine whether the statement is true or false....Ch. 13.5 - Determine whether the statement is true or false....Ch. 13.5 - Use Theorem 13.5.3 to find dy/dx and check your...Ch. 13.5 - Use Theorem 13.5.3 to find dy/dx and check your...Ch. 13.5 - Use Theorem 13.5.3 to find dy/dx and check your...Ch. 13.5 - Use Theorem 13.5.3 to find dy/dx and check your...Ch. 13.5 - Find z/xandz/y by implicit differentiation, and...Ch. 13.5 - Find z/xandz/y by implicit differentiation, and...Ch. 13.5 - Find z/xandz/y by implicit differentiation, and...Ch. 13.5 - Find z/xandz/y by implicit differentiation, and...Ch. 13.5 - (a) Suppose that z=fuandu=gx,y. Draw a tree...Ch. 13.5 - Prob. 50ESCh. 13.5 - Prob. 51ESCh. 13.5 - Prob. 52ESCh. 13.5 - Prob. 53ESCh. 13.5 - Let f be a differentiable function of one...Ch. 13.5 - Let z=fxy,yx. show that z/x+z/y=0.Ch. 13.5 - Prob. 56ESCh. 13.5 - Suppose that the equation z=fx,y is expressed in...Ch. 13.5 - Prob. 58ESCh. 13.5 - Prob. 59ESCh. 13.5 - Prob. 60ESCh. 13.5 - Prob. 61ESCh. 13.5 - Prob. 62ESCh. 13.5 - Let w=lner+es+et+eu. Show that wrstu=6er+s+t+u4wCh. 13.5 - Prob. 64ESCh. 13.5 - (a) Let w be a differentiable function of...Ch. 13.5 - Let w=x12+x22++xn2k,wheren2. for what values of k...Ch. 13.5 - Derive the identity ddxhxgxftdt=fgxgxfhxhx by...Ch. 13.5 - Prove. If f,fx,andfy are continuous on a circular...Ch. 13.5 - Prove: If fxx,y=0andfyx,y=0 throughout a circular...Ch. 13.5 - Compare the use of the formula dydx=f/xf/y with...Ch. 13.6 - The gradient of fx,y,z=xy2z3 at the point 1,1,1 is...Ch. 13.6 - Suppose that the differentiable function fx,y has...Ch. 13.6 - If the gradient of fx,y at the origin is 6i+8j,...Ch. 13.6 - If the gradient of then fx,y,zat1,2,3is2i2j+k, the...Ch. 13.6 - Find Duf at P. fx,y=1+xy3/2;P3,1;u=12i+12jCh. 13.6 - Find Duf at P. fx,y=sin5x3y;P3,5;u=35i45jCh. 13.6 - Find Duf at P. fx,y=ln1+x2+y;P0,0;u=110i310jCh. 13.6 - Find Duf at P. fx,y=cx+dyxy;P3,4;u=45i+35jCh. 13.6 - Prob. 5ESCh. 13.6 - Find Duf at P. fx,y,z=yexz+z2;P0,2,3;u=27i37j+67kCh. 13.6 - Find Duf at P....Ch. 13.6 - Find Duf at P. fx,y,z=sinxyz;P12,13,;u=13i13j+13kCh. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of f at P in the...Ch. 13.6 - Find the directional derivative of fatP in the...Ch. 13.6 - Find the directional derivative of fatP in the...Ch. 13.6 - Find the directional derivative of fatP in the...Ch. 13.6 - Find the directional derivative of fatP in the...Ch. 13.6 - Find the directional derivative of fx,y=xx+y at...Ch. 13.6 - Find the directional derivative of...Ch. 13.6 - Find the directional derivative of fx,y=xyeyatP1,1...Ch. 13.6 - Let fx,y=yx+y Find a unit vector u for which...Ch. 13.6 - Find the directional derivative of fx,y,z=yx+z at...Ch. 13.6 - Find the directional derivative of the function...Ch. 13.6 - Prob. 29ESCh. 13.6 - Prob. 30ESCh. 13.6 - Prob. 31ESCh. 13.6 - The accompanying figure shows some level curves of...Ch. 13.6 - Find zorw. z=sin7y27xyCh. 13.6 - Find zorw. z=7sin6x/yCh. 13.6 - Find zorw. z=6x+7y6x7yCh. 13.6 - Prob. 36ESCh. 13.6 - Prob. 37ESCh. 13.6 - Find zorw. w=xe8ysin6zCh. 13.6 - Prob. 39ESCh. 13.6 - Find zorw. w=e5xsecx2yzCh. 13.6 - Find the gradient of f at the indicated point....Ch. 13.6 - Find the gradient of f at the indicated point....Ch. 13.6 - Find the gradient of f at the indicated point....Ch. 13.6 - Find the gradient of f at the indicated point....Ch. 13.6 - Find the gradient of f at the indicated point....Ch. 13.6 - Find the gradient of f at the indicated point....Ch. 13.6 - Sketch the level curve of fx,y that passes through...Ch. 13.6 - Sketch the level curve of fx,y that passes through...Ch. 13.6 - Sketch the level curve of fx,y that passes through...Ch. 13.6 - Sketch the level curve of fx,y that passes through...Ch. 13.6 - Find a unit vector u that is normal at P1,2 to the...Ch. 13.6 - Find a unit vector u that is normal at P2,3 to the...Ch. 13.6 - Prob. 53ESCh. 13.6 - Prob. 54ESCh. 13.6 - Prob. 55ESCh. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Prob. 58ESCh. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Prob. 61ESCh. 13.6 - Prob. 62ESCh. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Prob. 65ESCh. 13.6 - Find a unit vector in the direction in which f...Ch. 13.6 - Determine whether the statement is true or false....Ch. 13.6 - Determine whether the statement is true or false....Ch. 13.6 - Prob. 69ESCh. 13.6 - Prob. 70ESCh. 13.6 - Given that f4,5=2ij, find the directional...Ch. 13.6 - Given that fx0,y0=i2j and Dufx0,y0=2, find u (two...Ch. 13.6 - The accompanying figure shows some level curves of...Ch. 13.6 - The accompanying figure shows a topographic map of...Ch. 13.6 - Let z=3x2y2. Find all points at which z=6.Ch. 13.6 - Given that z=3x+y2, find z at the point 5,2.Ch. 13.6 - A particle moves along a path C given by the...Ch. 13.6 - The temperature (in degrees Celsius) at a point...Ch. 13.6 - If the electric potential at a point x,y in the...Ch. 13.6 - On a certain mountain, the elevation z above a...Ch. 13.6 - Given that the directional derivative of fx,y,z at...Ch. 13.6 - Prob. 82ESCh. 13.6 - Let r=x2+y2....Ch. 13.6 - Use the formula in part (b) of Exercise 83 to find...Ch. 13.6 - Let ur be a unit vector whose counterclockwise...Ch. 13.6 - Prove: If fandg are differentiable, then...Ch. 13.6 - A heat-seeking particle is located at the point P...Ch. 13.6 - A heat-seeking particle is located at the point P...Ch. 13.6 - Use a graphing utility to generate the trajectory...Ch. 13.6 - Use a graphing utility to generate the trajectory...Ch. 13.6 - (a) Use a CAS to graph fx,y=x2+3y2ex2+y2. (b) At...Ch. 13.6 - Prove: If x=xtandy=yt are differentiable at t, and...Ch. 13.6 - Prove: If f,fx,andfy are continuous on a circular...Ch. 13.6 - Prob. 94ESCh. 13.6 - Given that the functions...Ch. 13.7 - Prob. 1QCECh. 13.7 - Prob. 2QCECh. 13.7 - An equation for the tangent plane to the graph of...Ch. 13.7 - The sphere x2+y2+z2=9 and the plane x+y+z=5...Ch. 13.7 - Consider the ellipsoid x2+y2+4z2=12. (a) Find an...Ch. 13.7 - Consider the surface xzyz3+yz2=2. (a) Find an...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find an equation for the tangent plane and...Ch. 13.7 - Find all points on the surface at which the...Ch. 13.7 - Find a point on the surface z=3x2y2 at which the...Ch. 13.7 - Find a point on the surface z=83x22y2 at which the...Ch. 13.7 - Show that the surfaces z=x2+y2andz=110x2+y2+52...Ch. 13.7 - (a) Find all points of intersection of the line...Ch. 13.7 - Show that if f is differentiable and z=xfx/y, then...Ch. 13.7 - Determine whether the statement is true or false....Ch. 13.7 - Determine whether the statement is true or false....Ch. 13.7 - Determine whether the statement is true or false....Ch. 13.7 - Prob. 22ESCh. 13.7 - Prob. 23ESCh. 13.7 - Find two unit vectors that are normal to the given...Ch. 13.7 - Show that every line that is normal to the sphere...Ch. 13.7 - Find all points on the ellipsoid 2x2+3y2+4z2=9 at...Ch. 13.7 - Prob. 27ESCh. 13.7 - Show that the ellipsoid 2x2+3y2+z2=9 and the...Ch. 13.7 - Find parametric equations for the tangent line to...Ch. 13.7 - Find parametric equations for the tangent line to...Ch. 13.7 - Find parametric equations for the tangent line to...Ch. 13.7 - The accompanying figure shows the intersection of...Ch. 13.7 - Show that the equation of the plane that is...Ch. 13.7 - Show that the equation of the plane that is...Ch. 13.7 - Prove: If the surfaces z=fx,yandz=gx,y intersect...Ch. 13.7 - Use the result in Exercise 35 to show that the...Ch. 13.7 - Two surface fx,y,z=0andgx,y,z=0 are said to be...Ch. 13.7 - Use the result of Exercise 37 to show that the...Ch. 13.7 - Show that the volume of the solid bounded by the...Ch. 13.7 - Discuss the role of the chain rule in defining a...Ch. 13.7 - Discuss the relationship between tangent planes...Ch. 13.8 - The critical points of the function fx,y=x3+xy+y2...Ch. 13.8 - Prob. 2QCECh. 13.8 - Prob. 3QCECh. 13.8 - A rectangular box has total surface area of 2ft2....Ch. 13.8 - Locate all absolute maxima and minima, if any, by...Ch. 13.8 - Locate all absolute maxima and minima, if any, by...Ch. 13.8 - Complete the squares and locate all absolute...Ch. 13.8 - Complete the squares and locate all absolute...Ch. 13.8 - The contour plots show all significant features of...Ch. 13.8 - The contour plots show all significant features of...Ch. 13.8 - The contour plots show all significant features of...Ch. 13.8 - The contour plots show all significant features of...Ch. 13.8 - Prob. 9ESCh. 13.8 - Prob. 10ESCh. 13.8 - Prob. 11ESCh. 13.8 - Prob. 12ESCh. 13.8 - Prob. 13ESCh. 13.8 - Locate all relative maxima, relative minima, and...Ch. 13.8 - Prob. 15ESCh. 13.8 - Prob. 16ESCh. 13.8 - Locate all relative maxima, relative minima, and...Ch. 13.8 - Locate all relative maxima, relative minima, and...Ch. 13.8 - Prob. 19ESCh. 13.8 - Prob. 20ESCh. 13.8 - Use a CAS to generate a contour plot of...Ch. 13.8 - Use a CAS to generate a contour plot of...Ch. 13.8 - Prob. 23ESCh. 13.8 - Prob. 24ESCh. 13.8 - Prob. 25ESCh. 13.8 - Prob. 26ESCh. 13.8 - (a) Show that the second partials test provides no...Ch. 13.8 - (a) Show that the second partials test provides no...Ch. 13.8 - Recall from Theorem 4.4.4 that if a continuous...Ch. 13.8 - If f is a continuous function of one variable with...Ch. 13.8 - Prob. 31ESCh. 13.8 - Prob. 32ESCh. 13.8 - Prob. 33ESCh. 13.8 - Find the absolute extrema of the given function on...Ch. 13.8 - Prob. 35ESCh. 13.8 - Find the absolute extrema of the given function on...Ch. 13.8 - Find three positive numbers whose sum is 48 and...Ch. 13.8 - Find three positive numbers whose sum is 27 and...Ch. 13.8 - Find all points on the portion of the plane...Ch. 13.8 - Prob. 40ESCh. 13.8 - Find the dimensions of the rectangular box of...Ch. 13.8 - An international airline has a regulation that...Ch. 13.8 - A closed rectangular box with a volume of 16ft3 is...Ch. 13.8 - A manufacturer makes two models of an item,...Ch. 13.8 - Consider the function fx,y=4x23y2+2xy over the...Ch. 13.8 - Show that among all parallelograms with perimeter...Ch. 13.8 - Determine the dimensions of a rectangular box,...Ch. 13.8 - A length of sheet metal 27 inches wide is to be...Ch. 13.8 - A common problem in experimental work is to obtain...Ch. 13.8 - A common problem in experimental work is to obtain...Ch. 13.8 - Use the formulas obtained in Exercises 49 to find...Ch. 13.8 - Use the formulas obtained in Exercises 49 to find...Ch. 13.8 - Use the formulas obtained in Exercises 49 to find...Ch. 13.8 - Use the formulas obtained in Exercises 49 to find...Ch. 13.8 - The following table shows the life expectancy by...Ch. 13.8 - A company manager wants to establish a...Ch. 13.8 - If a gas is cooled with its volume held constant,...Ch. 13.8 - Find (a) a continuous function fx,y that is...Ch. 13.8 - Prob. 59ESCh. 13.8 - Explain how to determine the location of relative...Ch. 13.9 - (a) Suppose that fx,yandgx,y are differentiable at...Ch. 13.9 - The maximum value of x+y subject to the constraint...Ch. 13.9 - The maximum value of x+y+z subject to the...Ch. 13.9 - The maximum and minimum values of 2x+3y subject to...Ch. 13.9 - The accompanying figure shows graphs of the line...Ch. 13.9 - The accompanying figure shows the graphs of the...Ch. 13.9 - (a) On a graphing utility, graph the circle...Ch. 13.9 - (a) If you have a CAS with implicit plotting...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Use Lagrange multipliers to find the maximum and...Ch. 13.9 - Prob. 13ESCh. 13.9 - Determine whether the statement is true or false....Ch. 13.9 - Determine whether the statement is true or false....Ch. 13.9 - Determine whether the statement is true or false....Ch. 13.9 - Solve using Lagrange multipliers. Find the point...Ch. 13.9 - Solve using Lagrange multipliers. Find the point...Ch. 13.9 - Solve using Lagrange multipliers. Find the point...Ch. 13.9 - Prob. 20ESCh. 13.9 - Solve using Lagrange multipliers. Find the points...Ch. 13.9 - Prob. 22ESCh. 13.9 - Solve using Lagrange multipliers. Find a vector in...Ch. 13.9 - Prob. 24ESCh. 13.9 - Use Lagrange multipliers to solve the indicated...Ch. 13.9 - Use Lagrange multipliers to solve the indicated...Ch. 13.9 - Use Lagrange multipliers to solve the indicated...Ch. 13.9 - Prob. 28ESCh. 13.9 - Use Lagrange multipliers to solve the indicated...Ch. 13.9 - Use Lagrange multipliers to solve the indicated...Ch. 13.9 - Prob. 31ESCh. 13.9 - Prob. 32ESCh. 13.9 - Let ,,and be the angles of a triangle. (a) Use...Ch. 13.9 - The accompanying figure shows the intersection of...Ch. 13 - Let f(x,y)=exlny.Find (a)f(lny,ex)(b)f(r+s,rs).Ch. 13 - Sketch the domain of f using solid lines for...Ch. 13 - Show that the level curves of the cone z=x2+y2 and...Ch. 13 - (a) In words, describe the level surfaces of the...Ch. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Let z=fx,y. (a) Express z/x and z/y as limits. (b)...Ch. 13 - The pressure in newtons per square meter N/m2 of a...Ch. 13 - Find the slope of the tangent line at the point...Ch. 13 - Verify the assertion. If =tan(x2+y2)+xy,thenxy=yx.Ch. 13 - Verify the assertion. If...Ch. 13 - Verify the assertion. If F(x,y,z)=2z33(x2+y2)z,...Ch. 13 - Verify the assertion. If...Ch. 13 - What do fanddf represent, and how are they...Ch. 13 - If =x2y2xy+y2x, find the increment and the...Ch. 13 - Use differentials to estimate the change in the...Ch. 13 - Find the local linear approximation of...Ch. 13 - Suppose that z is a difierentiable function of x...Ch. 13 - In each part. use, Theorem 13.5.3 to find dy/dx....Ch. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - (a) How are the directional derivative and the...Ch. 13 - In words, what does the derivative Duf(x0,y0) tell...Ch. 13 - Find Duf(3,5)forf(x,y)=yln(x+y)ifu=35i+45j.Ch. 13 - Suppose that f(0,0)=2i+32j. (a) Find a unit vector...Ch. 13 - At the point (1,2), the directional derivative Duf...Ch. 13 - Find equations for the tangent plane and normal...Ch. 13 - Find all points P0 on the surface z=2xy at which...Ch. 13 - Shows that for all tangent planes to the surface...Ch. 13 - Find all points on the paraboloid z=9x2+4y2 at...Ch. 13 - Suppose the equations of motion of a particle are...Ch. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Solve these exercises two ways: (a) Use the...Ch. 13 - Prob. 39RECh. 13 - In economics, a production model is a mathematical...Ch. 13 - In economics, a production model is a mathematical...Ch. 13 - In economics, a production model is a mathematical...
Additional Math Textbook Solutions
Find more solutions based on key concepts
A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. Hint...
A First Course in Probability (10th Edition)
1. combination of numbers, variables, and operation symbols is called an algebraic______.
Algebra and Trigonometry (6th Edition)
Testing Hypotheses. In Exercises 13-24, assume that a simple random sample has been selected and test the given...
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
Read about basic ideas of statistics in Common Core Standards for grades 3-5, and discuss why students at these...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
NOTE: Write your answers using interval notation when appropriate.
CHECKING ANALYTIC SKILLS Fill in each blank ...
Graphical Approach To College Algebra
The equivalent expression of x(y+z) by using the commutative property.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Suppose a raindrop evaporates as it falls but maintains its spherical shape. Assume that the rate at which the raindrop evaporates (that is, the rate at which it loses mass) is proportional to its surface area, where the constant of proportionality is –0.01. The density (mass per volume) of water at 3.98°C is 1 g/cm3. The surface area of a sphere is 4πr2, and its volume is 4πr3/3, where r is the radius. Assume no air resistance. (Project 8 models the motion of this raindrop under the influence of air resistance.) Assume that the initial radius is 0.3 cm. Determine the raindrop’s initial mass. Write a differential equation for the rate of change of mass as a function of r. Write an equation for r as a function of massarrow_forwardConsider a water tank that is being filled with rainfall at the top and is drained through a small hole at the bottom. The change in volume can be modelled by considering the amount of water entering and leaving the tank (per unit of time) as follows dV dt fin - fout. Here volume of water in the tank V is in litres, flow rate in fin is in litres per hour, flow rate out fout is. in litres per hour and time t is in hours. Initially, the tank contains 50L of water: V(0) = 50. (a) Assume the rainfall throughout the day is getting heavier, such that, fin(t) = 10 + t and that the tank is losing 10% of its volume of water per hour, such that, fout (V) = 0.1V. Check by direct substitution that the function V(t) = 10(t + 5e-0.1t) satisfies the ODE and the initial condition. (b) Now assume that the hole is slowly growing in size, so that the flow rate out increases with time: fout (V, t) = 0.1(1 + 0.1t) V. Solve the ordinary differential equation for V(t) with this flow rate out, using either…arrow_forwardLet f (x, y, z) = xln(yz). Find the maximum rate of change of f at the point (1,2,) and the direction in which it occurs. %3Darrow_forward
- Write the differential for y = (3x − 1)³. 2 dy = 9(x − 1)² dx - - О dy = 9(3x − 1)² dx - О dy = (9x − 3)² dx – 2 dy = 3(3x − 1)² dx -arrow_forwardEvaluate ∆yA and ∆y if y=x2+2x+1 at x=1 and dx = 0.1.arrow_forward(Underdamped) A body weighing 100 lb (mass m = 3.125 slugs in fps units) is oscillating attached to a spring and a dashpot. Its first two maximum displacements of 6.73in. and 1.46 in. are observed to occur at times 0.34 s and 1.17 s, respectively. Compute the damping constant (in pound-seconds per foot) and spring constant (in pounds per foot).arrow_forward
- The specific gravity of a substance is given by G = DS/DW, where DS is the density of thesubstance in kg/m³ and DW is the density of water, which is known to be 1000 kg/m³. Thedensity of a particular substance is measured to be DS = 500 ± 5 kg/m³. Estimate the specific gravity, and find the uncertainty in the estimate.arrow_forwardA. We are given the acceleration function of a particle to be alt) = -9.8 m/ s2.If vl0) = 30m/s find the function vlt) using the fact that ult) is the antiderivative of S %3D alt). B. Using ult) above, compute the net change in distance (displacement) the particle made from O to 5 seconds. Use the Net Change formula and the fact that s ' (t) = vlt). C. Using ult) obtained above and the average function formula to obtain the average velocity of the particle from O to 5 seconds.arrow_forward7 Determine the gradient function of y = Vx '. %3Darrow_forward
- An object of mass m moves at a constant speed v in a circular path of radius r. The force required to produce the centripetal component of acceleration is called the centripetal force and is given by F = mv2/r. Newton's Law of Universal Gravitation is given by F = GMm/d2, where d is the distance between the centers of the two bodies of masses M and m, and G is a gravitational constant. The speed required for circular motion is v = √ GM/r. Use the result above to find the speed necessary for the given circular orbit around Earth. Let GM = 9.56 x 104 cubic miles per second per second, and assume the radius of Earth is 4000 miles. (Round your answer to two decimal places.) The orbit of a communications satellite R miles above the surface of Earth that is in geosynchronous orbit. [The satellite completes one orbit per side real day (approximately 23 hours, 56 minutes), and therefore appears to remain stationary above a point on Earth.] X mi/sarrow_forwardDo just part f urgent solution requiredarrow_forwardvt e dtarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
03a: Numerical Differentiation Review; Author: Jaisohn Kim;https://www.youtube.com/watch?v=IMYsqbV4CEg;License: Standard YouTube License, CC-BY