2. Find $\lim _{h \rightarrow 0} \frac{x^{2}-(x+h)^{2}}{h}$.
Solution: This equals $\lim _{h \rightarrow 0} \frac{x^{2}-x^{2}-h^{2}-2 h x}{h}=\lim _{h \rightarrow 0}-h-2 x=-2 x$. Alternate Solution: This is the definition of the derivative of $-x^{2}$ with respect to $x$, which is $-2 x$.