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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781305266636

Chapter 3.9, Problem 52E

Textbook Problem

Draw a graph of *f* and use it to make a rough sketch of the antiderivative that passes through the origin.

**52.**
*x* ≤ 3

Expert Solution

To determine

**To sketch:** The graph of the function

The given function is an even function.

Use the equation of function

Thus, the graph of the function

The antiderivative function passes through the origin.

Refer to the Figure 1 in Part (a) for the graph of the function

As the graph of the function

Single Variable Calculus

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What is the...Ch. 3.7 - What is the maximum vertical distance between the...Ch. 3.7 - What is the minimum vertical distance between the...Ch. 3.7 - Find the dimensions of a rectangle with perimeter...Ch. 3.7 - Find the dimensions of a rectangle with area 1000...Ch. 3.7 - A model used for the yield Y of an agricultural...Ch. 3.7 - The rate (in mg carbon/m3/h) at which...Ch. 3.7 - Consider the following problem: A farmer with 750...Ch. 3.7 - Consider the following problem: A box with an open...Ch. 3.7 - A farmer wants to fence in an area of 1.5 million...Ch. 3.7 - A box with a square base and open top must have a...Ch. 3.7 - If 1200 cm2 of material is available to make a box...Ch. 3.7 - A rectangular storage container with an open top...Ch. 3.7 - Do Exercise 16 assuming the container has a lid...Ch. 3.7 - A farmer wants to fence in a rectangular plot of...Ch. 3.7 - If the farmer in Exercise 18 wants to enclose 8000...Ch. 3.7 - (a) Show that of all the rectangles with a given...Ch. 3.7 - Find the point on the line y = 2x + 3 that is...Ch. 3.7 - Find the point on the curve y=x that is closest to...Ch. 3.7 - Find the points on the ellipse 4x2 + y2 = 4 that...Ch. 3.7 - Find, correct to two decimal places, the...Ch. 3.7 - Find the dimensions of the rectangle of largest...Ch. 3.7 - Find the area of the largest rectangle that can be...Ch. 3.7 - Find the dimensions of the rectangle of largest...Ch. 3.7 - Find the area of the largest trapezoid that can be...Ch. 3.7 - Find the dimensions of the isosceles triangle of...Ch. 3.7 - If the two equal sides of an isosceles triangle...Ch. 3.7 - A right circular cylinder is inscribed in a sphere...Ch. 3.7 - A right circular cylinder is inscribed in a cone...Ch. 3.7 - A right circular cylinder is inscribed in a sphere...Ch. 3.7 - A Norman window has the shape of a rectangle...Ch. 3.7 - The top and bottom margins of a poster are each 6...Ch. 3.7 - A poster is to have an area of 180 in2 with 1-inch...Ch. 3.7 - A piece of wire 10 m long is cut into two pieces....Ch. 3.7 - Solve Exercise 37 if one piece is bent into a...Ch. 3.7 - If you are offered one slice from a round pizza...Ch. 3.7 - A fence 8 ft tall runs parallel to a tall building...Ch. 3.7 - A cone-shaped drinking cup is made from a circular...Ch. 3.7 - A cone-shaped paper drinking cup is to be made to...Ch. 3.7 - A cone with height h is inscribed in a larger cone...Ch. 3.7 - An object with weight W is dragged along a...Ch. 3.7 - If a resistor of R ohms is connected across a...Ch. 3.7 - For a fish swimming at a speed v relative to the...Ch. 3.7 - In a beehive, each cell is a regular hexagonal...Ch. 3.7 - A boat leaves a dock at 2:00 pm and travels due...Ch. 3.7 - Solve the problem in Example 4 if the river is 5...Ch. 3.7 - A woman at a point A on the shore of a circular...Ch. 3.7 - An oil refinery is located on the north bank of a...Ch. 3.7 - Suppose the refinery in Exercise 51 is located 1...Ch. 3.7 - The illumination of an object by a light source is...Ch. 3.7 - Find an equation of the line through the point (3,...Ch. 3.7 - Let a and b be positive numbers. Find the length...Ch. 3.7 - At which points on the curve y = 1 + 40x3 3x5...Ch. 3.7 - What is the shortest possible length of the line...Ch. 3.7 - What is the smallest possible area of the triangle...Ch. 3.7 - (a) If C(x) is the cost of producing x units of a...Ch. 3.7 - (a) Show that if the profit P(x) is a maximum,...Ch. 3.7 - A baseball team plays in a stadium that holds...Ch. 3.7 - During the summer months Terry makes and sells...Ch. 3.7 - A retailer has been selling 1200 tablet computers...Ch. 3.7 - A company operates 16 oil wells in a designated...Ch. 3.7 - Show that of all the isosceles triangles with a...Ch. 3.7 - Consider the situation in Exercise 51 if the cost...Ch. 3.7 - Consider the tangent line to the ellipse...Ch. 3.7 - The frame for a kite is to be made from six pieces...Ch. 3.7 - A point P needs to be located somewhere on the...Ch. 3.7 - The graph shows the fuel consumption c of a car...Ch. 3.7 - Let v1 be the velocity of light in air and v2 the...Ch. 3.7 - Two vertical poles PQ and ST are secured by a rope...Ch. 3.7 - The upper right-hand corner of a piece of paper,...Ch. 3.7 - A steel pipe is being carried down a hallway 9 ft...Ch. 3.7 - An observer stands at a point P, one unit away...Ch. 3.7 - A rain gutter is to be constructed from a metal...Ch. 3.7 - Find the maximum area of a rectangle that can be...Ch. 3.7 - The blood vascular system consists of blood...Ch. 3.7 - Ornithologists have determined that some species...Ch. 3.7 - Two light sources of identical strength are placed...Ch. 3.8 - The figure shows the graph of a function f....Ch. 3.8 - Follow the instructions for Exercise 1(a) but use...Ch. 3.8 - Suppose the tangent line to the curve y = f(x) at...Ch. 3.8 - For each initial approximation, determine...Ch. 3.8 - For which of the initial approximations x1 = a, b,...Ch. 3.8 - Use Newtons method with the specified initial...Ch. 3.8 - Use Newtons method with the specified initial...Ch. 3.8 - Use Newtons method with the specified initial...Ch. 3.8 - Use Newtons method with initial approximation x1 =...Ch. 3.8 - Use Newtons method with initial approximation x1 =...Ch. 3.8 - Use Newtons method to approximate the given number...Ch. 3.8 - Use Newtons method to approximate the given number...Ch. 3.8 - (a) Explain how we know that the given equation...Ch. 3.8 - 2x5 + 9x4 7x3 11x = 0, [3, 4]Ch. 3.8 - Use Newtons method to approximate the indicated...Ch. 3.8 - Use Newtons method to approximate the indicated...Ch. 3.8 - Use Newtons method to find all solutions of the...Ch. 3.8 - Use Newtons method to find all solutions of the...Ch. 3.8 - Use Newtons method to find all solutions of the...Ch. 3.8 - Use Newtons method to find all solutions of the...Ch. 3.8 - Use Newtons method to find all solutions of the...Ch. 3.8 - Use Newtons method to find all solutions of the...Ch. 3.8 - Use Newtons method to find all the solutions of...Ch. 3.8 - Use Newtons method to find all the solutions of...Ch. 3.8 - Use Newtons method to find all the solutions of...Ch. 3.8 - Use Newtons method to find all the solutions of...Ch. 3.8 - (a) Apply Newtons method to the equation x2 a = 0...Ch. 3.8 - (a) Apply Newtons method to the equation 1/x a =...Ch. 3.8 - Explain why Newtons method doesnt work for finding...Ch. 3.8 - (a) Use Newtons method with x1 = 1 to find the...Ch. 3.8 - Explain why Newtons method fails when applied to...Ch. 3.8 - If f(x)={xifx0xifx0 then the root of the equation...Ch. 3.8 - (a) Use Newtons method to find the critical...Ch. 3.8 - Use Newtons method to find the absolute maximum...Ch. 3.8 - Use Newtons method to find the coordinates of the...Ch. 3.8 - Of the infinitely many lines that are tangent to...Ch. 3.8 - Use Newtons method to find the coordinates,...Ch. 3.8 - In the figure, the length of the chord AB is 4 cm...Ch. 3.8 - A car dealer sells a new car for 18,000. He also...Ch. 3.8 - The figure shows the sun located at the origin and...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the most general antiderivative of the...Ch. 3.9 - Find the antiderivative F of f that satisfies the...Ch. 3.9 - Find the antiderivative F of f that satisfies the...Ch. 3.9 - Find f. 23. f(x) = 20x3 12x2 + 6xCh. 3.9 - Find f. 24. f(x) = x6 4x4 + x + 1 2342 Find f.Ch. 3.9 - f(x)=4x3Ch. 3.9 - Find f. 26. f(x) = x2/3 + x2/3Ch. 3.9 - Find f. 27. f(t) = 12 + sin tCh. 3.9 - Find f. 28. f(t)=t2costCh. 3.9 - Find f. 29. f(x)=1+3x,f(4)=25Ch. 3.9 - Find f. 30. f(x) = 5x4 3x2 + 4, f(1) = 2Ch. 3.9 - Find f. 31. f(x)=x(6+5x),f(1)=10Ch. 3.9 - Find f. 32. f(t) = t + 1/t3, t 0, f(1) = 6Ch. 3.9 - Find f. 33. f(t) = sec t (sec t + tan t), /2 t ...Ch. 3.9 - Find f. 34. f(x)=(x+1)/x,f(1)=5Ch. 3.9 - Find f. 35. f(x) = 2 + 12x 12x2, f(0) = 4, f(0) =...Ch. 3.9 - Find f. 36. f(x) = 8x3 + 5, f(1) = 0, f(1) = 8Ch. 3.9 - Find f. 37. f() = sin + cos , f(0) = 3, f(0) = 4Ch. 3.9 - Find f. 38. f(t) = 4 6/t4, f(1) = 6, f(2) = 9, t ...Ch. 3.9 - Find f. 39. f(x) = 4 + 6x + 24x2, f(0) = 3, f(1) =...Ch. 3.9 - Find f. 40. f(x) = 20x3 + 12x2 + 4, f(0) = 8, f(1)...Ch. 3.9 - Find f. 41. f(t)=t3cost,f(0)=2,f(1)=2Ch. 3.9 - Find f. 42. f(x) = cos x, f(0) = 1, f(0) = 2, f(0)...Ch. 3.9 - Given that the graph of f passes through the point...Ch. 3.9 - Find a function f such that f(x) = x3 and the line...Ch. 3.9 - The graph of a function f is shown. Which graph is...Ch. 3.9 - The graph of a function f is shown. Which graph is...Ch. 3.9 - The graph of a function is shown in the figure....Ch. 3.9 - The graph of the velocity function of a particle...Ch. 3.9 - The graph of f is shown in the figure. Sketch the...Ch. 3.9 - (a) Use a graphing device to graph f(x)=2x3x. (b)...Ch. 3.9 - Draw a graph of f and use it to make a rough...Ch. 3.9 - Draw a graph of f and use it to make a rough...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A particle is moving with the given data. Find the...Ch. 3.9 - A stone is dropped from the upper observation deck...Ch. 3.9 - Show that for motion in a straight line with...Ch. 3.9 - An object is projected upward with initial...Ch. 3.9 - Two balls are thrown upward from the edge of the...Ch. 3.9 - A stone was dropped off a cliff and hit the ground...Ch. 3.9 - If a diver of mass m stands at the end of a diving...Ch. 3.9 - A company estimates that the marginal cost (in...Ch. 3.9 - The linear density of a rod of length 1 m is given...Ch. 3.9 - Since raindrops grow as they fall, their surface...Ch. 3.9 - A car is traveling at 50 mi/h when the brakes are...Ch. 3.9 - What constant acceleration is required to increase...Ch. 3.9 - A car braked with a constant deceleration of 16...Ch. 3.9 - A car is traveling at 100 km/h when the driver...Ch. 3.9 - A model rocket is fired vertically upward from...Ch. 3.9 - A high-speed bullet train accelerates and...Ch. 3 - Explain the difference between an absolute maximum...Ch. 3 - What does the Extreme Value Theorem say?Ch. 3 - (a) State Fermats Theorem. (b) Define a critical...Ch. 3 - Explain how the Closed Interval Method works.Ch. 3 - (a) State Rolles Theorem. (b) State the Mean Value...Ch. 3 - (a) State the Increasing/Decreasing Test. (b) What...Ch. 3 - (a) State the First Derivative Test. (b) State the...Ch. 3 - Explain the meaning of each of the following...Ch. 3 - If you have a graphing calculator or computer, why...Ch. 3 - (a) Given an initial approximation x1 to a root of...Ch. 3 - (a) What is an antiderivative of a function f? (b)...Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Find the local and absolute extreme values of the...Ch. 3 - Find the local and absolute extreme values of the...Ch. 3 - Find the local and absolute extreme values of the...Ch. 3 - Find the local and absolute extreme values of the...Ch. 3 - Find the local and absolute extreme values of the...Ch. 3 - Find the local and absolute extreme values of the...Ch. 3 - Find the limit. 7. limx3x4+x56x42x2+1Ch. 3 - Find the limit. 8. limtt3t+2(2t1)(t2+t+1)Ch. 3 - Find the limit. 9. limx4x2+13x1Ch. 3 - Find the limit. 10. limx(x2+x3)Ch. 3 - Find the limit. 11. limx(4x2+3x2x)Ch. 3 - Find the limit. 12. limxsin4xxCh. 3 - Sketch the graph of a function that satisfies the...Ch. 3 - Sketch the graph of a function that satisfies the...Ch. 3 - Sketch the graph of a function that satisfies the...Ch. 3 - The figure shows the graph of the derivative f of...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Use the guidelines of Section 3.5 to sketch the...Ch. 3 - Produce graphs of f that reveal all the important...Ch. 3 - Produce graphs of f that reveal all the important...Ch. 3 - Produce graphs of f that reveal all the important...Ch. 3 - Produce graphs of f that reveal all the important...Ch. 3 - Show that the equation 3x + 2 cos x + 5 = 0 has...Ch. 3 - Suppose that f is continuous on [0, 4], f(0) = 1,...Ch. 3 - By applying the Mean Value Theorem to the function...Ch. 3 - For what values of the constants a and b is (1, 3)...Ch. 3 - Let g(x) = f(x2), where f is twice differentiable...Ch. 3 - Find two positive integers such that the sum of...Ch. 3 - Show that the shortest distance from the point...Ch. 3 - Find the point on the hyperbola xy = 8 that is...Ch. 3 - Find the smallest possible area of an isosceles...Ch. 3 - Find the volume of the largest circular cone that...Ch. 3 - In ABC, D lies on AB, CD AB, |AD| = |BD| = 4 cm,...Ch. 3 - Solve Exercise 43 when |CD| = 2 cm. 43. In ABC, D...Ch. 3 - The velocity of a wave of length L in deep water...Ch. 3 - A metal storage tank with volume V is to be...Ch. 3 - A hockey team plays in an arena with a seating...Ch. 3 - A manufacturer determines that the cost of making...Ch. 3 - Use Newtons method to find the root of the...Ch. 3 - Use Newtons method to find all solutions of the...Ch. 3 - Use Newtons method to find the absolute maximum...Ch. 3 - Use the guidelines in Section 3.5 to sketch the...Ch. 3 - Find the most general antiderivative of the...Ch. 3 - Find the most general antiderivative of the...Ch. 3 - Find f. 55. f(t) = 2t 3 sin t, f(0) = 5Ch. 3 - Find f. 56. f(u)=u2+uu,f(1)=3Ch. 3 - Find f. 57. f(x) = 1 6x + 48x2, f(0) = 1, f(0) =...Ch. 3 - Find f. 58. f(x) = 5x3 + 6x2 + 2, f(0) = 3, f(l) =...Ch. 3 - A particle is moving according to the given data....Ch. 3 - A particle is moving according to the given data....Ch. 3 - Use a graphing device to draw a graph of the...Ch. 3 - Investigate the family of curves given by...Ch. 3 - A canister is dropped from a helicopter 500 m...Ch. 3 - In an automobile race along a straight road, car A...Ch. 3 - A rectangular beam will be cut from a cylindrical...Ch. 3 - If a projectile is fired with an initial velocity...Ch. 3 - A light is to be placed atop a pole of height h...Ch. 3 - Show that sinxcosx2 for all x.Ch. 3 - Show that x2y2(4 x2)(4 y2) 16 for all numbers x...Ch. 3 - Show that the inflection points of the curve y =...Ch. 3 - Find the point on the parabola y = 1 x2 at which...Ch. 3 - Find the highest and lowest points on the curve x2...Ch. 3 - Water is flowing at a constant rate into a...Ch. 3 - Find the absolute maximum value of the function...Ch. 3 - Find a function f such that f(1)=12, f(0) = 0, and...Ch. 3 - If P(a, a2) is any point on the parabola y = x2,...Ch. 3 - An isosceles triangle is circumscribed about the...Ch. 3 - The line y = mx + b intersects the parabola y = x2...Ch. 3 - Sketch the graph of a function f such that f(x) 0...Ch. 3 - Determine the values of the number a for which the...Ch. 3 - Sketch the region in the plane consisting of all...Ch. 3 - Let ABC be a triangle with BAC = 120 and |AB| ...Ch. 3 - A triangle with sides a, b, and c varies with time...Ch. 3 - ABCD is a square piece of paper with sides of...Ch. 3 - The speeds of sound c1 in an upper layer and c2 in...Ch. 3 - For what values of c is there a straight line that...Ch. 3 - One of the problems posed by the Marquis de...Ch. 3 - Assume that a snowball melts so that its volume...Ch. 3 - A hemispherical bubble is placed on a spherical...

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