Volume and LengthSuppose that the increasing function ƒ(x)

Chapter 6, Problem 3AAE

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QUESTION:

Problem  3AAE

Volume and Length

Suppose that the increasing function ƒ(x) is smooth for x  0 and that .  Let s(x) denote the length of the graph of ƒ from (0, a) to (x, ƒ(x)), x > 0. Find ƒ(x) if s(x) = Cx for some constant C. What are the allowable values for C?

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QUESTION:

Problem  3AAE

Volume and Length

Suppose that the increasing function ƒ(x) is smooth for x  0 and that .  Let s(x) denote the length of the graph of ƒ from (0, a) to (x, ƒ(x)), x > 0. Find ƒ(x) if s(x) = Cx for some constant C. What are the allowable values for C?

ANSWER:

Solution:

Step 1 of 3:

In this problem, we need to find , if  for some constant C.Then find the allowable values of C.

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