Explanation The given function is y = x ( 1 − x 2 ) . It is known that, the points for which the graph crosses each axis is called the intercepts of the graph. Set y = 0 and obtain the x- intercept of the graph as follows: x ( 1 − x 2 ) = 0 Since the above equation is satisfied for of the curve y = x ( 1 − x 2 ) intercept on x -axis at x = 0 , − 1 , 1 . Set x = 0 in the curve and obtain the y- intercept of the graph as follows: Since the curve y = x ( 1 − x 2 ) is defined for x = 0 , the curve y = x ( 1 − x 2 ) intercept on y -axis. Thus, the given curve has x- intercept at x = 0 , − 1 , 1 and y- intercept at y = 0 . Obtain the symmetry of the given function as follows. Substitute, x = − x in the given equation y = x ( 1 − x 2 ) and check the symmetry of the given function as follows: Here, the curve y = x ( 1 − x 2 ) is not same as y = − x ( 1 − x 2 ) . Hence, the curve y = x ( 1 − x 2 ) is symmetric about y -axis. It is to be noted that, the curve y = x ( 1 − x 2 ) is not same as − y = x ( 1 − x 2 ) . Thus, the curve y = x ( 1 − x 2 ) is not symmetric about x-axis. Obtain the asymptotes of the given function as follows. As x → ∞ or x → − ∞ , the curve y = x ( 1 − x 2 ) tends to the graph of y = ∞ . Thus, there are no horizontal asymptote of the graph. Since the function y = x ( 1 − x 2 ) is defined for x = 0 , y → 0 hence there are no vertical asymptote of the graph. It is to be noted that, the function y = x ( 1 − x 2 ) is defined for all real numbers. Thus, the domain of the function is ( − 1 , 1 ) . The function y = x ( 1 − x 2 ) attains positive and negative values. Thus, the range of the function y = x ( 1 − x 2 ) is ( − 0.707 , 0.707 )

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 24.6, Problem 15E

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To sketch: The graph of the function y=x(1−x2).

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Chapter 24.6, Problem 14E

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Chapter 24 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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A microprocessor chip is being designed with a...Ch. 24.7 - Prob. 18E Ch. 24.7 - What are the dimensions of the largest rectangular...Ch. 24.7 - A rectangular storage area is to be constructed...Ch. 24.7 - Prob. 21E Ch. 24.7 - Prob. 22E Ch. 24.7 - Prob. 23E Ch. 24.7 - Prob. 24E Ch. 24.7 - Prob. 25E Ch. 24.7 - Prob. 26E Ch. 24.7 - Prob. 27E Ch. 24.7 - Prob. 28E Ch. 24.7 - Prob. 29E Ch. 24.7 - Prob. 30E Ch. 24.7 - Prob. 31E Ch. 24.7 - Prob. 32E Ch. 24.7 - Prob. 33E Ch. 24.7 - What is the minimum slope of the curve y = x5 −...Ch. 24.7 - Prob. 35E Ch. 24.7 - Prob. 36E Ch. 24.7 - Prob. 37E Ch. 24.7 - Prob. 38E Ch. 24.7 - Prob. 39E Ch. 24.7 - Prob. 40E Ch. 24.7 - Prob. 41E Ch. 24.7 - Computer simulation shows that the drag F (in N)...Ch. 24.7 - Prob. 43E Ch. 24.7 - The potential energy E of an electric charge q due...Ch. 24.7 - An open box is to be made from a square piece of...Ch. 24.7 - Prob. 46E Ch. 24.7 - Prob. 47E Ch. 24.7 - Prob. 48E Ch. 24.7 - An oil pipeline is to be built from a refinery to...Ch. 24.7 - 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Prob. 48RE Ch. 24 - Prob. 49RE Ch. 24 - Prob. 50RE Ch. 24 - Prob. 51RE Ch. 24 - Prob. 52RE Ch. 24 - In Exercises 49–94, solve the given problems. 53....Ch. 24 - Prob. 54RE Ch. 24 - Prob. 55RE Ch. 24 - Prob. 56RE Ch. 24 - The deflection y (in m) of a beam at a horizontal...Ch. 24 - Prob. 58RE Ch. 24 - Prob. 59RE Ch. 24 - Prob. 60RE Ch. 24 - Prob. 61RE Ch. 24 - Prob. 62RE Ch. 24 - In Fig. 24.75, the tension T supports the 40.0-N...Ch. 24 - Prob. 64RE Ch. 24 - Prob. 65RE Ch. 24 - Prob. 66RE Ch. 24 - An analysis of the power output P (in kW/m3) of a...Ch. 24 - The altitude h (in ft) of a certain rocket as a...Ch. 24 - Prob. 69RE Ch. 24 - Prob. 70RE Ch. 24 - Prob. 71RE Ch. 24 - Prob. 72RE Ch. 24 - Prob. 73RE Ch. 24 - A special insulation strip is to be sealed...Ch. 24 - Prob. 75RE Ch. 24 - Prob. 76RE Ch. 24 - Prob. 77RE Ch. 24 - Prob. 78RE Ch. 24 - Prob. 79RE Ch. 24 - Prob. 80RE Ch. 24 - Prob. 81RE Ch. 24 - Prob. 82RE Ch. 24 - Prob. 83RE Ch. 24 - Prob. 84RE Ch. 24 - Prob. 85RE Ch. 24 - Prob. 86RE Ch. 24 - 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The graph of the function y = x ( 1 − x 2 ) .

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Chapter 24 Solutions