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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)=cosx,x=0

Short Answer

Expert verified

(a) f'(c)=0

(b)f'(c)=0

Step by step solution

01

Part (a) Step 1. Given information.

Given function isf(x)=cosx

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,

limh0f(0+h)f(0)h=limh0cos(0+h)cos0h=limh0cos(h)1h=0

03

Part (b) Step 1. Find f'(c)

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

limx0f(x)f(0)x0=limx0cosxcos0x=limx0cosx1x=0

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