Explanation Given: f ( x ) = x N Formula used: f ' ( a ) = lim x → a f ( x ) − f ( a ) x − a 1 + r + r 2 + r 3 + ... + r N − 1 = 1 − r N 1 − r Calculation: f ' ( a ) = lim x → a f ( x ) − f ( a ) x − a = lim x → a x N − a N x − a = a N − 1 lim x → a ( x a ) N − 1 ( x a ) − 1 = a N − 1 lim r → 1 r N − 1 r − 1 ( substitute r = x a ) To evaluate the limit we use 1 + r + r 2 + r 3 + ...

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 11.2, Problem 67E

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How to show that $f^{'} (a) = \lim_{x \to a} \frac{x^{N} - a^{N}}{x - a} = a^{N - 1} \lim_{r \to 1} \frac{r^{N} - 1}{r - 1}$ .

We need to evaluate the limit.

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Chapter 11.2, Problem 66E

Chapter 11.2, Problem 68E

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Chapter 11 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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How to show that f ' ( a ) = lim x → a x N − a N x − a = a N − 1 lim r → 1 r N − 1 r − 1 . We need to evaluate the limit.

Solution Summary: The author explains how to prove that f'(a ) = lim x a

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How to show that $f^{'} (a) = \lim_{x \to a} \frac{x^{N} - a^{N}}{x - a} = a^{N - 1} \lim_{r \to 1} \frac{r^{N} - 1}{r - 1}$ .

We need to evaluate the limit.

Want to see the full answer?

Chapter 11 Solutions

How to show that f ' ( a ) = lim x → a x N − a N x − a = a N − 1 lim r → 1 r N − 1 r − 1 . We need to evaluate the limit.

Solution Summary: The author explains how to prove that f'(a ) = lim x a

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How to show that f'(a)=limx→axN−aNx−a=aN−1limr→1rN−1r−1. We need to evaluate the limit.

Want to see the full answer?

Chapter 11 Solutions

How to show that $f^{'} (a) = \lim_{x \to a} \frac{x^{N} - a^{N}}{x - a} = a^{N - 1} \lim_{r \to 1} \frac{r^{N} - 1}{r - 1}$ .

We need to evaluate the limit.