   Chapter 3.6, Problem 57E

Chapter
Section
Textbook Problem

# You just got your derivatives test back, and you can’t under- stand why that teacher of yours deducted so many points for what you thought was your best work: f ' ( a ) = lim h → 0 f ( x + h ) − f ( x ) h           = lim h → 0 f ( x ) + h − f ( x ) h          = lim h → 0 h h Canceled the f ( x )          = 1. X WRONG   − 10 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=limh0hh=1

Explanation

Given information:

The provided expression is as follows:

limh0f(x+h)f(x)h=limh0f(x)+hf(x)h=limh0hh=1

Consider the expression,

limh0f(x+h)f(x)h=limh0f(x)+hf(x)h=limh0hh=1<

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