## Calculus with Applications (10th Edition)

a. $x^{2}+2xh+h^{2}-3$ b. $2xh+h^{2}$ c. $2x+h$
$f(x)=x^{2}-3$ a. $f(x+h)=(x+h)^{2}-3=(x^{2}+2xh+h^{2})-3$ $=x^{2}+2xh+h^{2}-3$ b. $f(x+h)-f(x)$ $=(x^{2}+2xh+h^{2}-3)-(x^{2}-3)$ $=x^{2}+2xh+h^{2}-3-x^{2}+3$ $=2xh+h^{2}$ c. $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{2xh+h^{2}}{h}=\frac{h(2x+h)}{h}$ $=2x+h$