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Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

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Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
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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