Explanation The given function is v = ( r − 1 r 3 ) for k = 1 . It is known that, the points for which the graph crosses each axis is called the intercepts of the graph. Set v = 0 and obtain the x- intercept of the graph as follows: ( r − 1 r 3 ) = 0 Since the above equation is satisfied for value of r = − 1 , 1 the curve v = ( r − 1 r 3 ) intercept on horizontal axis. Set r = 0 in the curve v = ( r − 1 r 3 ) and obtain the v - intercept of the graph as follows: Since the curve v = ( r − 1 r 3 ) is not defined for r = 0 , the curve v = ( r − 1 r 3 ) does not intercept on vertical-axis. Thus, the given curve has horizontal - intercept and not v - intercept. Obtain the symmetry of the given function as follows. Substitute, r = − r in the given equation v = ( r − 1 r 3 ) and check the symmetry of the given function as follows: Here, the curve v = ( r − 1 r 3 ) is same as v = − ( r − 1 r 3 ) . Hence, the curve v = ( r − 1 r 3 ) is not symmetric about vertical-axis. It is to be noted that, the curve v = ( r − 1 r 3 ) is not same as − v = ( r − 1 r 3 ) . Thus, the curve v = ( r − 1 r 3 ) is not symmetric about horizontal-axis. Obtain the asymptotes of the given function as follows. As r → ∞ or r → − ∞ , the curve v = ( r − 1 r 3 ) tends to the graph of v → 0 . Thus, there are no horizontal asymptote of the graph. Since the function v = ( r − 1 r 3 ) is undefined for r = 0 , the vertical asymptote of the graph is r = 0 . It is to be noted that, the function v = ( r − 1 r 3 ) is defined for all real numbers except r = 0 . Thus, the domain of the function is ( − ∞ , ∞ ) − { 0 }

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 24.6, Problem 29E

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To sketch: The graph of the function v=k(r−1r3) for k=1 with the assumption that a raindrop is always spherical and as it falls its radius increases from 1 mm to r mm, and its velocity v (in mm/s) is v=k(r−1r3).

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Chapter 24.6, Problem 28E

Chapter 24.6, Problem 30E

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Chapter 24 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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The graph of the function v = k ( r − 1 r 3 ) for k=1 with the assumption that a raindrop is always spherical and as it falls its radius increases from 1 mm to r mm, and its velocity v (in mm/s) is v = k ( r − 1 r 3 ) .

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To sketch: The graph of the function v=k(r−1r3) for k=1 with the assumption that a raindrop is always spherical and as it falls its radius increases from 1 mm to r mm, and its velocity v (in mm/s) is v=k(r−1r3).

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Chapter 24 Solutions