Single Variable Calculus
Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Chapter 2.2, Problem 43E
To determine

To graph: The function f(x)=x+|x|, and conclude the differentiability of the points (−1,0) and (0,0).

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Chapter 2 Solutions

Single Variable Calculus

Ch. 2.1 - A curve has equation y = f(x). (a) Write an...Ch. 2.1 - Graph the curve y = sin x in the viewing...Ch. 2.1 - (a) Find the slope of the tangent line to the...Ch. 2.1 - (a) Find the slope of the tangent Line to the...Ch. 2.1 - Prob. 5ECh. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - (a) A particle starts by moving to the right along...Ch. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - If a rock is thrown upward on the planet Mars with...Ch. 2.1 - Prob. 15ECh. 2.1 - The displacement (in feet) of a particle moving in...Ch. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - If an equation of the tangent line to the curve y...Ch. 2.1 - Prob. 22ECh. 2.1 - Sketch the graph of a function f for which f(0) =...Ch. 2.1 - Sketch the graph of a function g for which g(0) =...Ch. 2.1 - Sketch the graph of a function g that is...Ch. 2.1 - Sketch the graph of a function f where the domain...Ch. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - (a) If F(x) = 5x/(1 + x2), find F(2) and use it to...Ch. 2.1 - (a) If G(x) = 4x2 x3, find G(a) and use it to...Ch. 2.1 - Find f(a). 31. f(t) = 3x2 4x + 1Ch. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Find f(a). 36. f(x)=41xCh. 2.1 - Each limit represents the derivative of some...Ch. 2.1 - Prob. 38ECh. 2.1 - Each limit represents the derivative of some...Ch. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - A roast turkey is taken from an oven when its...Ch. 2.1 - Researchers measured the average blood alcohol...Ch. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - The cost (in dollars) of producing x units of a...Ch. 2.1 - If a cylindrical tank holds 100.000 gallons of...Ch. 2.1 - Prob. 53ECh. 2.1 - The number of bacteria after t hours in a...Ch. 2.1 - Let H(t) be the daily cost (in dollar) to heat an...Ch. 2.1 - Prob. 56ECh. 2.1 - The quantity of oxygen that can dissolve in water...Ch. 2.1 - The graph shows the influence of the temperature T...Ch. 2.1 - Prob. 59ECh. 2.1 - Determine whether f(0) exists. 60....Ch. 2.1 - Prob. 61ECh. 2.2 - Use the given graph to estimate the value of each...Ch. 2.2 - Use the given graph to estimate the value of each...Ch. 2.2 - Match the graph of each function in (a)(d) with...Ch. 2.2 - Trace or copy the graph of the given function f....Ch. 2.2 - Trace or copy the graph of the given function f....Ch. 2.2 - Trace or copy the graph of the given function f....Ch. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Trace or copy the graph of the given function f....Ch. 2.2 - Prob. 12ECh. 2.2 - A rechargeable battery is plugged into a charger....Ch. 2.2 - The graph (from the US Department of Energy) shows...Ch. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Let f(x) = x3. (a) Estimate the values of f(0),...Ch. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Prob. 22ECh. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - (a) If f(x) = x + 1/x, find f(x). (b) Check to see...Ch. 2.2 - The unemployment rate U(t) varies with time. The...Ch. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Let P represent the percentage of a citys...Ch. 2.2 - Suppose N is the number of people in the United...Ch. 2.2 - The graph of f is given. State, with reasons, the...Ch. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - The figure shows the graphs of f, f, and f ....Ch. 2.2 - The figure shows graphs of f, f and f. Identify...Ch. 2.2 - The figure shows the graphs of three functions....Ch. 2.2 - Prob. 50ECh. 2.2 - Use the definition of a derivative to find f(x)...Ch. 2.2 - Prob. 52ECh. 2.2 - If f(x) = 2x2 x3, find f(x), f(x), f(x), and...Ch. 2.2 - (a) The graph of a position function of a car is...Ch. 2.2 - Let f(x)=x3. (a) If a 0, use Equation 2.1.5 to...Ch. 2.2 - Prob. 56ECh. 2.2 - Show that the function f(x) = |x 6| is not...Ch. 2.2 - Prob. 58ECh. 2.2 - (a) Sketch the graph of the function f(x) = x|x|....Ch. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Nick starts jogging and runs faster and faster for...Ch. 2.2 - When you turn on a hot-water faucet, the...Ch. 2.2 - Let be the tangent line to the parabola y = x2 at...Ch. 2.3 - Differentiate the function. 1. f(x) = 240Ch. 2.3 - Differentiate the function. 2. f(x) = 2Ch. 2.3 - Differentiate the function. 3. f(x) = 5.2x + 2.3Ch. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Differentiate the function. 6. f(t) = 1.4t5 2.5t2...Ch. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Differentiate the function. 11. F(r)=5r3Ch. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Differentiate the function. 16. S(R) = 4R2Ch. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Differentiate the function. 22. D(t)=1+16t2(4t)3Ch. 2.3 - Prob. 23ECh. 2.3 - Find the derivative of the function F(x)=x45x3+xx2...Ch. 2.3 - Differentiate. 25. f(x) = (5x2 2)(x3 + 3x)Ch. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Differentiate. 35. y=sss2Ch. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Differentiate. 40. A(v) = v2/3(2v2 + 1 v2)Ch. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - The general polynomial of degree n has the form...Ch. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Find an equation of the tangent line to the curve...Ch. 2.3 - Prob. 53ECh. 2.3 - (a) The curve y = x/(1 + x2) is called a...Ch. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.3 - Biologists have proposed a cubic polynomial to...Ch. 2.3 - Prob. 66ECh. 2.3 - Prob. 67ECh. 2.3 - Prob. 68ECh. 2.3 - Prob. 69ECh. 2.3 - Prob. 70ECh. 2.3 - If f(x)=xg(x), where g(4) = 8 and g(4) = 7, find...Ch. 2.3 - Prob. 72ECh. 2.3 - Prob. 73ECh. 2.3 - Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F...Ch. 2.3 - Prob. 75ECh. 2.3 - Prob. 76ECh. 2.3 - Prob. 77ECh. 2.3 - For what values of x does the graph of f(x) = x3 +...Ch. 2.3 - Prob. 79ECh. 2.3 - Prob. 80ECh. 2.3 - Find equations of both lines that are tangent to...Ch. 2.3 - Prob. 82ECh. 2.3 - Prob. 83ECh. 2.3 - Where does the normal line to the parabola y = x2 ...Ch. 2.3 - Prob. 85ECh. 2.3 - (a) Find equations of both lines through the point...Ch. 2.3 - Prob. 87ECh. 2.3 - Find the nth derivative of each function by...Ch. 2.3 - Find a second-degree polynomial P such that P(2) =...Ch. 2.3 - The equation y + y 2y = x3 is called a...Ch. 2.3 - Prob. 91ECh. 2.3 - Find a parabola with equation y = ax2 + bx + c...Ch. 2.3 - In this exercise we estimate the rate at which the...Ch. 2.3 - Prob. 94ECh. 2.3 - Prob. 95ECh. 2.3 - Prob. 96ECh. 2.3 - Prob. 97ECh. 2.3 - Prob. 98ECh. 2.3 - Prob. 99ECh. 2.3 - Prob. 100ECh. 2.3 - For what values of a and b is the line 2x + y = b...Ch. 2.3 - Prob. 102ECh. 2.3 - Find the value of c such that the line y=32x+6 is...Ch. 2.3 - Let f(x)={x2ifx2mx+bifx2 Find the values of m and...Ch. 2.3 - An easy proof of the Quotient Rule can he given if...Ch. 2.3 - Prob. 106ECh. 2.3 - Evaluate limx1x10001x1.Ch. 2.3 - Prob. 108ECh. 2.3 - Prob. 109ECh. 2.3 - Sketch the parabolas y = x2 and y = x2 2x + 2. Do...Ch. 2.4 - Differentiate. 1. f(x) = x2 sin xCh. 2.4 - Prob. 2ECh. 2.4 - Differentiate. 3. f(x) = 3 cot x 2 cos xCh. 2.4 - Prob. 4ECh. 2.4 - Differentiate. 5. y = sec tanCh. 2.4 - Differentiate. 6. g(t) = 4 sec t + tan tCh. 2.4 - Prob. 7ECh. 2.4 - Differentiate. 8. y = u(a cos u + b cot u)Ch. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Differentiate. 11. f()=sin1+cosCh. 2.4 - Differentiate. 12. y=cosx1sinxCh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Differentiate. 15. f() = cos sinCh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - (a) If f(x) = sec x x, find f(x). (b) Check to...Ch. 2.4 - (a) If f(x)=xsinx, find f(x). (b) Check to see...Ch. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - For what values of x does the graph of f(x) = x +...Ch. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Find the limit. 46. limx0cscxsin(sinx)Ch. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Find the given derivative by finding the first few...Ch. 2.4 - Find the given derivative by finding the first few...Ch. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - A semicircle with diameter PQ sits on an isosceles...Ch. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Find the derivative of the function. 13. f() =...Ch. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Find the derivative of the function. 16. f(t) = t...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Find the derivative of the function. 24....Ch. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Find the derivative of the function. 32. J() =...Ch. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Find the derivative of the function. 36. y=xsin1xCh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Find the derivative of the function. 39. f(t) =...Ch. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Find the derivative of the function. 43. g(x) =...Ch. 2.5 - Find the derivative of the function. 44. y =...Ch. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Find y and y. 47. y = cos(sin 3)Ch. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - If g is a twice differentiable function and f(x) =...Ch. 2.5 - Prob. 71ECh. 2.5 - Prob. 72ECh. 2.5 - Find the given derivative by finding the first few...Ch. 2.5 - Find the given derivative by finding the first few...Ch. 2.5 - The displacement of a particle on a vibrating...Ch. 2.5 - Prob. 76ECh. 2.5 - A Cepheid variable star is a star whose brightness...Ch. 2.5 - In Example 1.3.4 we arrived at a model for the...Ch. 2.5 - Prob. 79ECh. 2.5 - Prob. 80ECh. 2.5 - Prob. 83ECh. 2.5 - Prob. 84ECh. 2.5 - Prob. 85ECh. 2.5 - Suppose y = f(x) is a curve that always lies above...Ch. 2.5 - Use the Chain Rule to show that if is measured in...Ch. 2.5 - Prob. 88ECh. 2.5 - If y = f(u) and u = g(x), where f and g are twice...Ch. 2.5 - Prob. 90ECh. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Find dy/dx by implicit differentiation. 16....Ch. 2.6 - Prob. 17ECh. 2.6 - Find dy/dx by implicit differentiation. 18. x sin...Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Regard y as the independent variable and x as the...Ch. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - (a) The curve with equation y2 = 5x4 x2 is called...Ch. 2.6 - (a) The curve with equation y2 = x3 + 3x2 is...Ch. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - If xy + y3 = 1, find the value of y at the point...Ch. 2.6 - If x2 + xy + y3 = 1, find the value of y at the...Ch. 2.6 - Find the points on the lemniscate in Exercise 31...Ch. 2.6 - Prob. 44ECh. 2.6 - Prob. 45ECh. 2.6 - Show that the sum of the x- and y-intercepts of...Ch. 2.6 - Prob. 47ECh. 2.6 - The Power Rule can be proved using implicit...Ch. 2.6 - Prob. 49ECh. 2.6 - Two curves are orthogonal if their tangent lines...Ch. 2.6 - Two curves are orthogonal if their tangent lines...Ch. 2.6 - Prob. 52ECh. 2.6 - Show that the ellipse x2/a2 + y2/b2 = 1 and the...Ch. 2.6 - Prob. 54ECh. 2.6 - Prob. 55ECh. 2.6 - Prob. 56ECh. 2.6 - The equation x2 xy + y2 = 3 represents a rotated...Ch. 2.6 - (a) Where does the normal line to the ellipse x2 ...Ch. 2.6 - Prob. 59ECh. 2.6 - Prob. 60ECh. 2.6 - Prob. 61ECh. 2.6 - The figure shows a lamp located three units to the...Ch. 2.7 - A particle moves according to a law of motion s =...Ch. 2.7 - A particle moves according to a law of motion s =...Ch. 2.7 - A particle moves according to a law of motion s =...Ch. 2.7 - A particle moves according to a law of motion s =...Ch. 2.7 - Prob. 5ECh. 2.7 - Graphs of the position functions of two particles...Ch. 2.7 - The height (in meters) of a projectile shot...Ch. 2.7 - If a ball is thrown vertically upward with a...Ch. 2.7 - If a rock is thrown vertically upward from the...Ch. 2.7 - Prob. 10ECh. 2.7 - (a) A company makes computer chips from square...Ch. 2.7 - Prob. 12ECh. 2.7 - (a) Find the average rate of change of the area of...Ch. 2.7 - A stone is dropped into a lake, creating a...Ch. 2.7 - A spherical balloon is being inflated. Find the...Ch. 2.7 - Prob. 16ECh. 2.7 - The mass of the part of a metal rod that lies...Ch. 2.7 - If a tank holds 5000 gallons of water, which...Ch. 2.7 - The quantity of charge Q in coulombs (C) that has...Ch. 2.7 - Newtons Law of Gravitation says that the magnitude...Ch. 2.7 - The force F acting on a body with mass m and...Ch. 2.7 - Some of the highest tides in the world occur in...Ch. 2.7 - Boyles Law states that when a sample of gas is...Ch. 2.7 - Prob. 24ECh. 2.7 - The table gives the population of the world P(t),...Ch. 2.7 - The table shows how the average age of first...Ch. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - The cost function for a certain commodity is...Ch. 2.7 - If p(x) is the total value of the production when...Ch. 2.7 - If R denotes the reaction of the body to some...Ch. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - In the study of ecosystems, predator-prey models...Ch. 2.7 - Prob. 36ECh. 2.8 - Prob. 1ECh. 2.8 - (a) If A is the area of a circle with radius r and...Ch. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - The radius of a sphere is increasing at a rate of...Ch. 2.8 - Prob. 7ECh. 2.8 - The area of a triangle with sides of lengths a and...Ch. 2.8 - Prob. 9ECh. 2.8 - Prob. 10ECh. 2.8 - Prob. 11ECh. 2.8 - A particle is moving along a hyperbola xy = 8. As...Ch. 2.8 - (a) What quantities are given in the problem? (b)...Ch. 2.8 - Prob. 14ECh. 2.8 - (a) What quantities are given in the problem? (b)...Ch. 2.8 - Prob. 16ECh. 2.8 - Two cars start moving from the same point. One...Ch. 2.8 - A spotlight on the ground shines on a wall 12 m...Ch. 2.8 - A man starts walking north at 4 ft/s from a point...Ch. 2.8 - A baseball diamond is a square with side 90 ft. A...Ch. 2.8 - The altitude of a triangle is increasing at a rate...Ch. 2.8 - A boat is pulled into a dock by a rope attached to...Ch. 2.8 - At noon, ship A is 100 km west of ship B. Ship A...Ch. 2.8 - A particle moves along the curve y = 2 sin(x/2)....Ch. 2.8 - Prob. 25ECh. 2.8 - A trough is 10 ft long and its ends have the shape...Ch. 2.8 - A water trough is 10 m long and a cross-section...Ch. 2.8 - A swimming pool is 20 ft wide, 40 ft long, 3 ft...Ch. 2.8 - Gravel is being dumped from a conveyor belt at a...Ch. 2.8 - A kite 100 ft above the ground moves horizontally...Ch. 2.8 - The sides of an equilateral triangle are...Ch. 2.8 - How fast is the angle between the ladder and the...Ch. 2.8 - Prob. 33ECh. 2.8 - Prob. 34ECh. 2.8 - If the minute hand of a clock has length r (in...Ch. 2.8 - Prob. 36ECh. 2.8 - Boyles Law states that when a sample of gas is...Ch. 2.8 - When air expands adiabatically (without gaining or...Ch. 2.8 - Prob. 39ECh. 2.8 - Brain weight B as a function of body weight W in...Ch. 2.8 - Prob. 41ECh. 2.8 - Two carts, A and B, are connected by a rope 39 ft...Ch. 2.8 - A television camera is positioned 4000 ft from the...Ch. 2.8 - A lighthouse is located on a small island 3 km...Ch. 2.8 - A plane flies horizontally at an altitude of 5 km...Ch. 2.8 - A Ferris wheel with a radius of 10 m is rotating...Ch. 2.8 - A plane flying with a constant speed of 300 km/h...Ch. 2.8 - Two people start from the same point. One walks...Ch. 2.8 - Prob. 49ECh. 2.8 - The minute hand on a watch is 8 mm long and the...Ch. 2.9 - Find the linearization L(x) of the function at a....Ch. 2.9 - Find the linearization L(x) of the function at a....Ch. 2.9 - Prob. 3ECh. 2.9 - Prob. 4ECh. 2.9 - Prob. 5ECh. 2.9 - Prob. 6ECh. 2.9 - Prob. 7ECh. 2.9 - Prob. 8ECh. 2.9 - Prob. 9ECh. 2.9 - Prob. 10ECh. 2.9 - Prob. 11ECh. 2.9 - Prob. 12ECh. 2.9 - Prob. 13ECh. 2.9 - Prob. 14ECh. 2.9 - (a) Find the differential dy and (b) evaluate dy...Ch. 2.9 - (a) Find the differential dy and (b) evaluate dy...Ch. 2.9 - Prob. 17ECh. 2.9 - (a) Find the differential dy and (b) evaluate dy...Ch. 2.9 - Prob. 19ECh. 2.9 - Prob. 20ECh. 2.9 - Prob. 21ECh. 2.9 - Prob. 22ECh. 2.9 - Use a linear approximation (or differentials) to...Ch. 2.9 - Use a linear approximation (or differentials) to...Ch. 2.9 - Prob. 25ECh. 2.9 - Use a linear approximation (or differentials) to...Ch. 2.9 - Use a linear approximation (or differentials) to...Ch. 2.9 - Use a linear approximation (or differentials) to...Ch. 2.9 - Prob. 29ECh. 2.9 - Explain, in terms of linear approximations or...Ch. 2.9 - The edge of a cube was found to be 30 cm with a...Ch. 2.9 - Prob. 32ECh. 2.9 - Prob. 33ECh. 2.9 - Prob. 34ECh. 2.9 - (a) Use differentials to find a formula for the...Ch. 2.9 - Prob. 36ECh. 2.9 - Prob. 37ECh. 2.9 - When blood flows along a blood vessel, the flux F...Ch. 2.9 - Prob. 39ECh. 2.9 - Prob. 40ECh. 2.9 - Suppose that the only information we have about a...Ch. 2.9 - Suppose that we dont have a formula for g(x) but...Ch. 2 - Write an expression for the slope of the tangent...Ch. 2 - Prob. 2RCCCh. 2 - If y = f(x) and x changes from x1 to x2, write...Ch. 2 - Define the derivative f(a). Discuss two ways of...Ch. 2 - Prob. 5RCCCh. 2 - Prob. 6RCCCh. 2 - Prob. 7RCCCh. 2 - Prob. 8RCCCh. 2 - Prob. 9RCCCh. 2 - Prob. 10RCCCh. 2 - Prob. 11RCCCh. 2 - Prob. 12RCCCh. 2 - Prob. 1RQCh. 2 - Prob. 2RQCh. 2 - Prob. 3RQCh. 2 - Prob. 4RQCh. 2 - Determine whether the statement is true or false....Ch. 2 - Prob. 6RQCh. 2 - Prob. 7RQCh. 2 - Determine whether the statement is true or false....Ch. 2 - Prob. 9RQCh. 2 - Prob. 10RQCh. 2 - Prob. 11RQCh. 2 - Prob. 12RQCh. 2 - Determine whether the statement is true or false....Ch. 2 - Prob. 14RQCh. 2 - Determine whether the statement is true or false....Ch. 2 - The displacement (in meters) of an object moving...Ch. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - The figure shows the graphs of f, f, and f....Ch. 2 - Find a function f and a number a such that...Ch. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Calculate y. 18. y=(x+1x2)7Ch. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Calculate y. 25. y=sec21+tan2Ch. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Find equations of the tangent line and normal line...Ch. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Find a parabola y = ax2 + bx + c that passes...Ch. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Find f in terms of g. 68. f(x)=g(tanx)Ch. 2 - Prob. 69RECh. 2 - Find h in terms of f and g. 70. h(x)=f(x)g(x)Ch. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - A particle moves on a vertical line so that its...Ch. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - The cost, in dollars, of producing x units of a...Ch. 2 - Prob. 77RECh. 2 - A paper cup has the shape of a cone with height 10...Ch. 2 - A balloon is rising at a constant speed of 5 ft/s....Ch. 2 - A waterskier skis over the ramp shown in the...Ch. 2 - The angle of elevation of the sun is decreasing at...Ch. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Evaluate dy if y = x3 2x2 + 1, x = 2, and dx =...Ch. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Prob. 87RECh. 2 - Prob. 88RECh. 2 - Prob. 89RECh. 2 - Suppose f is a differentiable function such that...Ch. 2 - Prob. 91RECh. 2 - Show that the length of the portion of any tangent...Ch. 2 - Find points P and Q on the parabola y = 1 x2 so...Ch. 2 - Prob. 2PCh. 2 - Show that the tangent lines to the parabola y =...Ch. 2 - Prob. 4PCh. 2 - If f(x)=limtxsectsecxtx, find the value of f(/4).Ch. 2 - Find the values of the constants a and b such that...Ch. 2 - Prob. 7PCh. 2 - If f is differentiable at a, where a 0, evaluate...Ch. 2 - Prob. 9PCh. 2 - Find all values of c such that the parabolas y =...Ch. 2 - How many lines are tangent to both of the circles...Ch. 2 - If f(x)=x46+x45+21+x, calculate f(46)(3). Express...Ch. 2 - The figure shows a rotating wheel with radius 40...Ch. 2 - Tangent lines T1 and T2 are drawn at two points P1...Ch. 2 - Let T and N be the tangent and normal lines to the...Ch. 2 - Prob. 16PCh. 2 - Prob. 17PCh. 2 - Let P(x1, y1) be a point on the parabola y2 = 4px...Ch. 2 - Prob. 19PCh. 2 - If f and g are differentiable functions with f(0)...Ch. 2 - Prob. 21PCh. 2 - Given an ellipse x2/a2 + y2/b2 = 1, where a b,...Ch. 2 - Find the two points on the curve y = x4 2x2 x...Ch. 2 - Suppose that three points on the parabola y = x2...Ch. 2 - Prob. 25PCh. 2 - Prob. 26PCh. 2 - Prob. 27P
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY