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Chapter 2: Q. 35 (page 184)

Use (a) the h鈫�0 definition of the derivative and then (b) the z鈫抍 definition of the derivative to find f'(c) for each function f and value x = c.

f(x)=sin鈦�x,x=0

Short Answer

Expert verified

(a) f'(c)=1

(b)f'(c)=1

Step by step solution

01

Part (a) Step 1. Given information.

Given function isf(x)=sin鈦�x

We have to findf'(c)

02

Part (a) Step 2. Find the f'(c)

We have to find the derivative of the function using h鈫�0 definition,

Therefore,

limh鈫�0鈥�f(0+h)鈭�f(0)h=limh鈫�0鈥�sin鈦�(0+h)鈭�sin鈦�0h=limh鈫�0鈥�sin鈦�(h)h=1

03

Part (b) Step 1. Find f'(c)

Find the derivate of the function using x鈫�0 definition
Therefore,

limx鈫�0鈥�f(x)鈭�f(0)x鈭�0鈭�limx鈫�0鈥�sin鈦�x鈭�sin鈦�0x=limx鈫�0鈥�sin鈦�xx=1

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