   Chapter 2.R, Problem 87E

Chapter
Section
Textbook Problem

# 86–88 Express the limit as a derivative and evaluate. lim h → 0 16 + h 4 − 2 h

To determine

To evaluate:

Value of limit by expressing the limit as derivative

Solution:

limh016+h4-2h=132

Explanation

1. Concept:

Use derivative of a function f  at a number a

2. Formula:

(i)  Standard Formula:

f'x=limh0fx+h-f(x)h

(ii)  Power Rule:

ddxxn=n xn-1

3. Given:

limh016+h4-2h

4. Calculation:

limh016+h4-2h

We can express 2 as, 2=164

limh016+h4-164h

Comparing with standard formula, we find

fx+h=x+h4 ,fx=x4 and x=16

Therefore,

limh016+h4-164h=f'(16)

fx=x4=(x)14

Now, differentiating fx with respect to x

Using Power Rule

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