   Chapter 2.R, Problem 86E

Chapter
Section
Textbook Problem

# 86–88 Express the limit as a derivative and evaluate. lim x → 1 x 17 − 1 x − 1

To determine

To evaluate:

Value of limit by expressing the limit as derivative

Solution:

limx1x17-1x-1=17

Explanation

1. Concept:

Use derivative of a function f  at a number a

2. Formula:

(i)  Standard Formula:

f'a=limxafx-f(a)x-a

(ii)  Power Rule:

ddxxn=n xn-1

3. Given:

limx1x17-1x-1

4. Calculation:

limx1x17-1x-1

Comparing with standard formula we find,

a=1 and fx=x17

fa=f1=(1)17=1

Now, differentiating fx with respect to x,

By Standard Formula

limx&

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