The last part of Section 10.3 asks you to compute several different difference quotients. Some of the problems ask you to compute

$latex \underset{h \to 0}{\mathop{lim }},\frac{f(a+h)-f(a)}{h}$

where *f*(*x*) and *a* are given to you in the problem. Here are a few examples from the board.

$latex f(x)=4x+3$ and $latex a=1$

The board above contains a mistake…do you see where this group made a mistake?

$latex f(x)={{x}^{2}}-4$ and $latex a=1$

$latex f(x)={{x}^{2}}-1$ and $latex a=2$

In the examples below, you are asked to compute a difference quotient containing *x* instead of *a*.

Compute $latex \underset{h \to 0}{\mathop{lim }},\frac{f(x+h)-f(x)}{h}$ where $latex f(x)={{x}^{2}}+2x$

Compute $latex \underset{h \to 0}{\mathop{lim }},\frac{f(x+h)-f(x)}{h}$ where $latex f(x)={{x}^{2}}-x$

By the way, the correct solution to the first problem is below.

In this original calculation, *f*(*a*+*h*) and *f*(*a*) where switched.