Chapter 3.6, Problem 60E

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:

$\begin{array}{c}\underset{h\to 0}{\lim }\frac{f\left(x+h\right)-f\left(x\right)}{h}\\ =\underset{h\to 0}{\lim }\frac{f\left(x\right)+h-f\left(x\right)}{h}\\ =\underset{h\to 0}{\lim }\frac{f\left(x\right)+\cancel{h}-f\left(x\right)}{\cancel{h}}\text{ Now cancel the }h\\ =\underset{h\to 0}{\lim }f\left(x\right)-f\left(x\right)\text{ Canceled the }f\left(x\right)\end{array}$

$=0.$

$\text{X WRONG }-25$

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