   Chapter 10.6, Problem 60E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Your third friend just got her derivatives test back and can’t understand why that teacher of hers took off so many points for the following: lim h → 0 f ( x + h ) − f ( x ) h = lim h → 0 f ( x ) + h − f ( x ) h = lim h → 0 f ( x ) + h − f ( x ) h  Now cancel the  h = lim h → 0 f ( x ) − f ( x )   Canceled the  f ( x ) = 0. X WRONG   − 25 What was wrong with your answer? (There may be more than one error.)

To determine

The error in the following expression:

limh0f(x+h)f(x)h=limh0f(x)+hf(x)h=limh0f(x)+hf(x)h=limh0f(x)f(x)=0

Explanation

Given information:

The provided expression is as follows:

limh0f(x+h)f(x)h=limh0f(x)+hf(x)h=limh0f(x)+hf(x)h=limh0f(x)f(x)=0

Consider the expression,

limh0f(x+h)f(x)h=limh0f(x)+hf(x)h=limh0f(x)+hf(x)h

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