CALCULUS EARLY TRANSCENDENTALS W/ WILE
11th Edition
ISBN: 9781119228509
Author: Anton
Publisher: WILEY
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Textbook Question
Chapter 3.5, Problem 21ES
(a) Use the local linear approximation of
(b) How would you choose
(c) Approximate
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Students have asked these similar questions
(5) a) Find the linear and quadratic approximations of
sin(0.967) tan(0.267) + (0.96)²(0.26)
b) Compare these approximations with the actual value.
The force F (in pounds) on a person's back when he or she bends over at an angle from an upright position is modeled by
0.6W sin(+90°)
F =
sin(12⁰)
where W represents the person's weight (in pounds).
(a) Simplify the model.
F
(b) Use a graphing utility to graph the model, where W = 175 and 0° ≤ 0 ≤ 90°. At what angle (in degrees) is the force maximized?
A =
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At what angle (in degrees) is the force minimized?
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A rescued whale is released into the ocean 400 meters due east of a coast guard station. The whale swims directly away from the shore.
coast guard
station
point of
release
O tan(0)
(a) Which of the following equations can be used to relate the angle, 0, and the distance between the whale and the point of release, x?
O cos(0)
O sec(0) =
O sin(0)
=
O tan(0)
=
X
400
X
400
X
400
O cos² (0)-
X
400
400
X
O sec² (8) de
dt
de
dt
(b) Which of the following would be an appropriate related rate equation for the answer to part (a)?
1 dx
400 dt
=
O sec² (0) dx
dt
O sec(0)tan(0)-
O cos²(e) de
dt
=
=
8
1 dx
400 dt
de 1 dx
dt 400 dt
=
dx
dt
X
whale
1 de
400 dt
(c) If the whale swims at a constant rate of 60 meters per minute, how fast is the angle changing when the whale is 300 meters from the point of release? Give an exact answer.
radians per minute
Chapter 3 Solutions
CALCULUS EARLY TRANSCENDENTALS W/ WILE
Ch. 3.1 - The equation xy+2y=1 defines implicitly the...Ch. 3.1 - Use implicit differentiation to find dy/dx for...Ch. 3.1 - The slope of the tangent line to the graph of...Ch. 3.1 - Use implicit differentiation to find d2y/dx2 for...Ch. 3.1 - (a) Find dy/dx by differentiating implicitly. (b)...Ch. 3.1 - (a) Find dy/dx by differentiating implicitly. (b)...Ch. 3.1 - Find dy/dx by implicit differentiation. x2+y2=100Ch. 3.1 - Find dy/dx by implicit differentiation. x3+y3=3xy2Ch. 3.1 - Find dy/dx by implicit differentiation....Ch. 3.1 - Find dy/dx by implicit differentiation....
Ch. 3.1 - Find dy/dx by implicit differentiation. 1x+1y=1Ch. 3.1 - Find dy/dx by implicit differentiation. x2=x+yxyCh. 3.1 - Find dy/dx by implicit differentiation. sinx2y2=xCh. 3.1 - Find dy/dx by implicit differentiation. cosxy2=yCh. 3.1 - Find dy/dx by implicit differentiation....Ch. 3.1 - Find dy/dx by implicit differentiation....Ch. 3.1 - Find d2y/dx2 by implicit differentiation. 2x23y2=4Ch. 3.1 - Find d2y/dx2 by implicit differentiation. x3+y3=1Ch. 3.1 - Find d2y/dx2 by implicit differentiation. x3y34=0Ch. 3.1 - Find d2y/dx2 by implicit differentiation. xy+y2=2Ch. 3.1 - Find d2y/dx2 by implicit differentiation. y+siny=xCh. 3.1 - Find d2y/dx2 by implicit differentiation. xcosy=yCh. 3.1 - Find the slope of the tangent line to the curve at...Ch. 3.1 - Find the slope of the tangent line to the curve at...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - As shown in the accompanying figure, it appears...Ch. 3.1 - (a) A student claims that the ellipse x2xy+y2=1...Ch. 3.1 - (a) Use the implicit plotting capability of a CAS...Ch. 3.1 - Use implicit differentiation to find all points on...Ch. 3.1 - Find the values of a and b for the curve x2y+ay2=b...Ch. 3.1 - At what point(s) is the tangent line to the curve...Ch. 3.1 - Two curves are said to be orthogonal if their...Ch. 3.1 - Two curves are said to be orthogonal if their...Ch. 3.1 - (a) Use the implicit plotting capability of a CAS...Ch. 3.1 - (a) Use the implicit plotting capability of a CAS...Ch. 3.1 - Find dy/dx if 2y3t+t3y=1 and dtdx=1costCh. 3.1 - Find equations for two lines through the origin...Ch. 3.1 - A student asks: “Suppose implicit...Ch. 3.2 - The equation of the tangent line to the graph of...Ch. 3.2 - Find dy/dx . (a) y=ln3x (b) y=lnx (c) y=log1/xCh. 3.2 - Use logarithmic differentiation to find the...Ch. 3.2 - limh0ln1+hh=Ch. 3.2 - Find dy/dx . y=ln5xCh. 3.2 - Find .
Ch. 3.2 - Find dy/dx . y=ln1+xCh. 3.2 - Find dy/dx . y=ln2+xCh. 3.2 - Find dy/dx . y=lnx21Ch. 3.2 - Find dy/dx . y=lnx37x23Ch. 3.2 - Find .
Ch. 3.2 - Find dy/dx . y=ln1+x1xCh. 3.2 - Find .
Ch. 3.2 - Find dy/dx . y=lnx3Ch. 3.2 - Find dy/dx . y=lnxCh. 3.2 - Find .
Ch. 3.2 - Find dy/dx . y=xlnxCh. 3.2 - Find .
Ch. 3.2 - Find dy/dx . y=x2log232xCh. 3.2 - Find dy/dx . y=xlog2x22x3Ch. 3.2 - Find dy/dx . y=x21+logxCh. 3.2 - Find dy/dx . y=logx1+logxCh. 3.2 - Find dy/dx . y=lnlnxCh. 3.2 - Find dy/dx . y=lnlnlnxCh. 3.2 - Find dy/dx . y=lntanxCh. 3.2 - Find dy/dx . y=lncosxCh. 3.2 - Find dy/dx . y=coslnxCh. 3.2 - Find dy/dx . y=sin2lnxCh. 3.2 - Find dy/dx . y=logsin2xCh. 3.2 - Find dy/dx . y=log1sin2xCh. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find (a) ddxlogxe (b) ddxlogx2.Ch. 3.2 - Find (a) ddxlog1/xe (b) ddxloglnxe.Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - (a) Find the equation of a line through the origin...Ch. 3.2 - Use logarithmic differentiation to verify the...Ch. 3.2 - Find a formula for the area Aw of the triangle...Ch. 3.2 - Find a formula for the area Aw of the triangle...Ch. 3.2 - Verify that y=lnx+e satisfies dy/dx=ey , with y=1...Ch. 3.2 - Verify that y=lne2x satisfies dy/dx=ey , with y=2...Ch. 3.2 - Find a function 0 such that y=fx satisfies...Ch. 3.2 - Find a function f such that y=fx satisfies...Ch. 3.2 - Find the limit by interpreting the expression as...Ch. 3.2 - Find the limit by interpreting the expression as...Ch. 3.2 - Find the limit by interpreting the expression as...Ch. 3.2 - Modify the derivation of Equation (2) to give...Ch. 3.2 - Let p denote the number of paramecia in a nutrient...Ch. 3.2 - One model for the spread of information over time...Ch. 3.2 - Show that the formula for dy/dx obtained in the...Ch. 3.3 - Suppose that a one-to-one function f has tangent...Ch. 3.3 - In each case, from the given derivative, determine...Ch. 3.3 - Evaluate the derivative.
(a)
(b)
(c)
(d)
Ch. 3.3 - Let fx=ex3+x . Use fx to verify that f is...Ch. 3.3 - Let fx=x5+x3+x . (a) Show that f is one-to-one and...Ch. 3.3 - Let fx=x3+2ex . (a) Show that f is one-to-one and...Ch. 3.3 - Find f1x using Formula (2), and check your answer...Ch. 3.3 - Find f1x using Formula (2), and check your answer...Ch. 3.3 - Determine whether the function f is one-to-one by...Ch. 3.3 - Determine whether the function f is one-to-one by...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Complete each part to establish that the...Ch. 3.3 - Prove that the reflection about the line y=x of a...Ch. 3.3 - Suppose that and are increasing functions....Ch. 3.3 - Suppose that f and g are one-to-one functions....Ch. 3.3 - Find dy/dx . y=e7xCh. 3.3 - Find dy/dx . y=e5x2Ch. 3.3 - Find dy/dx . y=x3exCh. 3.3 - Find dy/dx . y=e1/xCh. 3.3 - Find dy/dx . y=exexex+exCh. 3.3 - Find dy/dx . y=sinexCh. 3.3 - Find dy/dx . y=extanxCh. 3.3 - Find dy/dx . y=exlnxCh. 3.3 - Find dy/dx . y=exe3xCh. 3.3 - Find dy/dx . y=exp1+5x3Ch. 3.3 - Find dy/dx . y=ln1xexCh. 3.3 - Find dy/dx . y=lncosexCh. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - (a) Explain why Formula (5) cannot be used to find...Ch. 3.3 - Find dy/dx using any method. y=x32x2+1exCh. 3.3 - Find dy/dx using any method. y=2x22x+1e2xCh. 3.3 - Find dy/dx using any method. y=x2+x3xCh. 3.3 - Find dy/dx using any method. y=x3+x35xCh. 3.3 - Find dy/dx using any method. y=43sinxexCh. 3.3 - Find dy/dx using any method. y=2cosx+lnxCh. 3.3 - Find dy/dx . y=sin13xCh. 3.3 - Find dy/dx . y=cos1x+12Ch. 3.3 - Find dy/dx . y=sin11/xCh. 3.3 - Find dy/dx . y=cos1cosxCh. 3.3 - Find dy/dx . y=tan1x3Ch. 3.3 - Find dy/dx . y=sec1x5Ch. 3.3 - Find dy/dx . y=tanx1Ch. 3.3 - Find dy/dx . y=1tan1xCh. 3.3 - Find dy/dx . y=exsec1xCh. 3.3 - Find dy/dx . y=lncos1xCh. 3.3 - Find dy/dx . y=sin1x+cos1xCh. 3.3 - Find dy/dx . y=x2sin1x3Ch. 3.3 - Find dy/dx . y=sec1x+csc1xCh. 3.3 - Find dy/dx . y=csc1exCh. 3.3 - Find dy/dx . y=cot1xCh. 3.3 - Find dy/dx . y=cot1xCh. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - (a) Use Formula (2) to prove that ddxcot1xx=0=1...Ch. 3.3 - (a) Use part (c) of Exercise 30 in Section 1.7 and...Ch. 3.3 - Find dy/dx by implicit differentiation....Ch. 3.3 - Find dy/dx by implicit differentiation....Ch. 3.3 - (a) Show that fx=x33x2+2x is not one-to-one on ,+...Ch. 3.3 - (a) Show that fx=x42x3 is not one-to-one on ,+ ....Ch. 3.3 - Let fx=x4+x3+1,0x2 . (a) Show that f is...Ch. 3.3 - Let fx=exp4x2x,x0 . (a) Show that f is one-to-one....Ch. 3.3 - Show that for any constant A and k , then function...Ch. 3.3 - Show that for any constants A and B , the function...Ch. 3.3 - Show that (a) y=xex satisfies the equation xy=1xy...Ch. 3.3 - Suppose that a new car is purchased for $20,000...Ch. 3.3 - Suppose that the percentage of U.S. households...Ch. 3.3 - Suppose that the population of oxygen-dependent...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Suppose that a steel ball bearing is released...Ch. 3.4 - If A=x2 and dxdt=3 , find dAdtx=10.Ch. 3.4 - If A=x2 and dAdt=3 , find dxdtx=10.Ch. 3.4 - A 10-foot ladder stands on a horizontal floor and...Ch. 3.4 - Suppose that a block of ice in the shape of a...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Let A be the area of a square whose sides have...Ch. 3.4 - Prob. 6ESCh. 3.4 - Let V be the volume of a cylinder having height h...Ch. 3.4 - Let l be the length of a diagonal of a rectangle...Ch. 3.4 - Let (in radians) be an acute angle in a right...Ch. 3.4 - Suppose that z=x3y2 , where both x and y are...Ch. 3.4 - The minute hand of a certain clock is 4in long....Ch. 3.4 - A stone dropped into a still pond sends out a...Ch. 3.4 - Oil spilled from a ruptured tanker spreads in a...Ch. 3.4 - A spherical balloon is inflated so that its volume...Ch. 3.4 - A spherical balloon is to be deflated so that its...Ch. 3.4 - A 17ft ladder is leaning against a wall. If the...Ch. 3.4 - A 13ft ladder is leaning against a wall. If the...Ch. 3.4 - A 10ft plank is leaning against a wall. If at a...Ch. 3.4 - A softball diamond is a square whose sides are...Ch. 3.4 - A rocket, rising vertically, is tracked by a radar...Ch. 3.4 - For the camera and rocket shown in Figure 3.4.5,...Ch. 3.4 - For the camera and rocket shown in Figure 3.4.5,...Ch. 3.4 - A satellite is in an elliptical orbit around the...Ch. 3.4 - An aircraft is flying horizontally at a constant...Ch. 3.4 - A conical water tank with vertex down has a radius...Ch. 3.4 - Grain pouring from a chute at the rate of 8ft3/min...Ch. 3.4 - Sand pouring from a chute forms a conical pile...Ch. 3.4 - Wheat is poured through a chute at the rate of...Ch. 3.4 - An aircraft is climbing at a 30 angle to the...Ch. 3.4 - A boat is pulled into a dock by means of a rope...Ch. 3.4 - For the boat in Exercise 30, how fast must the...Ch. 3.4 - A man 6ft tall is walking at the rate of 3ft/s...Ch. 3.4 - A beacon that makes one revolution every 10s is...Ch. 3.4 - An aircraft is flying at a constant altitude with...Ch. 3.4 - Solve Exercise 34 under the assumption that the...Ch. 3.4 - A police helicopter is flying due north at 100mi/h...Ch. 3.4 - Prob. 37ESCh. 3.4 - A point P is moving along the curve whose equation...Ch. 3.4 - A point P is moving along the line whose equation...Ch. 3.4 - Prob. 40ESCh. 3.4 - A particle is moving along the curve y=x/x2+1 ....Ch. 3.4 - A new design for a wind turbine adjusts the length...Ch. 3.4 - The thin lens equation in physics is 1s+1S=1f...Ch. 3.4 - Water is stored in a cone-shaped reservoir (vertex...Ch. 3.4 - A meteor enters the Earth’s atmosphere and bums...Ch. 3.4 - On a certain clock the minute hand is 4in long and...Ch. 3.4 - Coffee is poured at a uniform rate of 20cm3/s into...Ch. 3.5 - The local linear approximation of f at x0 use the ...Ch. 3.5 - Find an equation for the local linear...Ch. 3.5 - Let y=5x2 . Find dy and y at x=2 with dx=x=0.1 .Ch. 3.5 - Prob. 4QCECh. 3.5 - (a) Use Formula (1) to obtain the local linear...Ch. 3.5 - (a) Use Formula (1) to obtain the local linear...Ch. 3.5 - (a) Find the local linear approximation of the...Ch. 3.5 - A student claims that whenever a local linear...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - (a) Use the local linear approximation of sinx at...Ch. 3.5 - (a) Use the local linear approximation of at to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - The approximation 1+xk1+kx is commonly used by...Ch. 3.5 - Use the approximation 1+xk1+kx , along with some...Ch. 3.5 - Referring to the accompanying figure, suppose that...Ch. 3.5 - Prob. 37ESCh. 3.5 - (a) Let y=x . Find dy and y at x=9 with dx=x=1 ....Ch. 3.5 - Find formulas for and .
Ch. 3.5 - Find formulas for and .
Ch. 3.5 - Find formulas for dy and y . y=x22x+1Ch. 3.5 - Find formulas for and .
Ch. 3.5 - Find the differential dy . (a) y=4x37x2 (b)...Ch. 3.5 - Find the differential .
(a)
(b)
Ch. 3.5 - Find the differential dy . (a) y=x1x (b) y=1+x17Ch. 3.5 - Find the differential dy . (a) y=1x31 (b) y=1x32xCh. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Use the differential to approximate when ...Ch. 3.5 - Use the differential dy to approximate y when x...Ch. 3.5 - Use the differential dy to approximate y when x...Ch. 3.5 - Use the differential dy to approximate y when x...Ch. 3.5 - The side of a square is measured to be 10ft , with...Ch. 3.5 - The side of a cube is measured to be 25cm , with a...Ch. 3.5 - The hypotenuse of a right triangle is known to be...Ch. 3.5 - One side of a right triangle is known to be 25cm...Ch. 3.5 - The electrical resistance R of a certain wire is...Ch. 3.5 - A long high-voltage power line is 18feet above the...Ch. 3.5 - The area of a right triangle with a hypotenuse of...Ch. 3.5 - The side of a square is measured with a possible...Ch. 3.5 - The side of a cube is measured with a possible...Ch. 3.5 - The volume of a sphere is to be computed from a...Ch. 3.5 - The area of a circle is to be computed from a...Ch. 3.5 - A steel cube with 1-inch sides is coated with...Ch. 3.5 - A metal rod 15cm long and 5cm in diameter is to be...Ch. 3.5 - The time required for one complete oscillation of...Ch. 3.5 - The magnitude R of an earthquake on the Richter...Ch. 3.5 - Suppose that the time T (in days) for a cancerous...Ch. 3.5 - Explain why the local linear approximation of a...Ch. 3.6 - Prob. 1QCECh. 3.6 - Evaluate each of the limits in Quick Check...Ch. 3.6 - Using L’Hopital’s rule, limx+ex500x2=.Ch. 3.6 - Evaluate the given limit without using...Ch. 3.6 - Evaluate the given limit without using...Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Find the limits. limx0ex1sinxCh. 3.6 - Find the limits. limx0sin2xsin5xCh. 3.6 - Prob. 9ESCh. 3.6 - Find the limits. limt0tet1etCh. 3.6 - Prob. 11ESCh. 3.6 - Prob. 12ESCh. 3.6 - Find the limits. limx+lnxxCh. 3.6 - Find the limits. limx+e3xx2Ch. 3.6 - Find the limits. limx0+cotxlnxCh. 3.6 - Find the limits. limx0+1lnxe1/xCh. 3.6 - Find the limits. limx+x100exCh. 3.6 - Find the limits. limx0+lnsinxlntanxCh. 3.6 - Find the limits. limx0sin12xxCh. 3.6 - Find the limits. limx0xtan1xx3Ch. 3.6 - Find the limits. limx+xexCh. 3.6 - Find the limits. limxxtan12xCh. 3.6 - Find the limits. limx+xsinxCh. 3.6 - Find the limits. limx0+tanxlnxCh. 3.6 - Prob. 25ESCh. 3.6 - Find the limits. limxxcotxCh. 3.6 - Find the limits. limx+13/xxCh. 3.6 - Find the limits. limx01+2x3/xCh. 3.6 - Prob. 29ESCh. 3.6 - Find the limits. limx+1+a/xbxCh. 3.6 - Prob. 31ESCh. 3.6 - Find the limits. limx+cos2/xx2Ch. 3.6 - Find the limits. limx0cscx1/xCh. 3.6 - Find the limits. limx01x2cos3xx2Ch. 3.6 - Find the limits. limx+x2+xxCh. 3.6 - Find the limits. limx01x1ex1Ch. 3.6 - Find the limits. limx+xlnx2+1Ch. 3.6 - Find the limits. limx+lnxln1+xCh. 3.6 - Find the limits. limx0+xsinxCh. 3.6 - Find the limits. limx0+e2x1xCh. 3.6 - Find the limits. limx0+1lnxxCh. 3.6 - Find the limits. limx+x1/xCh. 3.6 - Find the limits. limx+lnx1/xCh. 3.6 - Find the limits. limx0+lnxxCh. 3.6 - Prob. 45ESCh. 3.6 - Show that for any positive integer n (a)...Ch. 3.6 - (a) Find the error in the following calculation:...Ch. 3.6 - (a) Find the error in the following calculation:...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Prob. 57ESCh. 3.6 - There is a myth that circulates among beginning...Ch. 3.6 - Verify that L’Hopital’s rule is of no help in...Ch. 3.6 - Verify that L’Hopital’s rule is of no help in...Ch. 3.6 - Verify that L’Hopital’s rule is of no help in...Ch. 3.6 - Verify that L’Hopital’s rule is of no help in...Ch. 3.6 - The accompanying schematic diagram represents an...Ch. 3.6 - (a) Show that limx/2/2xtanx=1 . (b) Show that...Ch. 3.6 - (a) Use a CAS to show that if k is a positive...Ch. 3.6 - Find all values of k and l such that...Ch. 3.6 - Let fx=x2sin1/x . (a) Are the limits limx0+fx and...Ch. 3.6 - (a) Explain why L’Hopital’s rule does not...Ch. 3.6 - Find limx0+xsin1/xsinx if it exists.Ch. 3.6 - Suppose that functions f and g are differentiable...Ch. 3.6 - Were we to use L’Hopital’s mle to evaluate...Ch. 3 - (a) Find dy/dx by differentiating implicitly, (b)...Ch. 3 - (a) Find dy/dx by differentiating implicitly, (b)...Ch. 3 - Find dy/dx by implicit differentiation. 1y+1x=1Ch. 3 - Find dy/dx by implicit differentiation. x3y3=6xyCh. 3 - Find dy/dx by implicit differentiation. secxy=yCh. 3 - Find dy/dx by implicit differentiation....Ch. 3 - Find d2y/dx2 by implicit differentiation. 3x24y2=7Ch. 3 - Find d2y/dx2 by implicit differentiation. 2xyy2=3Ch. 3 - Use implicit differentiation to find the slope of...Ch. 3 - At what point(s) is the tangent line to the curve...Ch. 3 - Prove that if P and Q are two distinct points on...Ch. 3 - Find the coordinates of the point in the first...Ch. 3 - Find the coordinates of the point in the first...Ch. 3 - Use implicit differentiation to show that the...Ch. 3 - Find dy/dx by first using algebraic properties of...Ch. 3 - Find dy/dx by first using algebraic properties of...Ch. 3 - Find dy/dx . y=ln2xCh. 3 - Find dy/dx . y=lnx2Ch. 3 - Find dy/dx . y=lnx+13Ch. 3 - Find dy/dx . y=lnx+13Ch. 3 - Find dy/dx . y=loglnxCh. 3 - Find dy/dx . y=1+logx1logxCh. 3 - Find dy/dx . y=lnx3/21+x4Ch. 3 - Find dy/dx . y=lnxcosx1+x2Ch. 3 - Find dy/dx . y=elnx2+1Ch. 3 - Find dy/dx . y=ln1+ex+e2x1e3xCh. 3 - Find dy/dx . y=2xexCh. 3 - Find dy/dx . y=a1+bexCh. 3 - Find dy/dx . y=1tan12xCh. 3 - Find dy/dx . y=2sin1xCh. 3 - Find dy/dx . y=xexCh. 3 - Find dy/dx . y=1+x1/xCh. 3 - Find dy/dx . y=sec12x+1Ch. 3 - Find dy/dx . y=cos1x2Ch. 3 - Find dy/dx using logarithmic differentiation....Ch. 3 - Find dy/dx using logarithmic differentiation....Ch. 3 - (a) Make a conjecture about the shape of the graph...Ch. 3 - Recall from Section 1.8 that the loudness of a...Ch. 3 - A particle is moving along the curve y=xlnx . Find...Ch. 3 - Find the equation of the tangent fine to the graph...Ch. 3 - Find the value of b so that the line y=x is...Ch. 3 - In each part, find the value of k for which the...Ch. 3 - If f and g are inverse functions and f is...Ch. 3 - In each part, find f1x using Formula (2) of...Ch. 3 - Find a point on the graph of y=e3x at which the...Ch. 3 - Show that the rate of change of y=5000e1.07x is...Ch. 3 - Show that the rate of change of y=32x57x is...Ch. 3 - The equilibrium constant k of a balanced chemical...Ch. 3 - Show that the function y=eaxsinbx satisfies...Ch. 3 - Show that the function y=tan1x satisfies...Ch. 3 - Suppose that the population of deer on an island...Ch. 3 - In each part, find each limit by interpreting the...Ch. 3 - Suppose that limfx= and limgx= . In each of the...Ch. 3 - (a) Under what conditions will a limit of the form...Ch. 3 - Evaluate the given limit. limx+exx2Ch. 3 - Evaluate the given limit. limx1lnxx41Ch. 3 - Evaluate the given limit. limx0x2e2sin23xCh. 3 - Evaluate the given limit. limx0ax1x,a0Ch. 3 - An oil slick on a lake is surrounded by a floating...Ch. 3 - The hypotenuse of a right triangle is growing at a...Ch. 3 - In each part, use the given information to find...Ch. 3 - Use an appropriate local linear approximation to...Ch. 3 - The base of the Great Pyramid at Giza is a square...
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