91Ó°ÊÓ

For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and righthand limits of the function given as \(x\) approaches \(a\). If the function has a limit as \(x\) approaches \(a\), state it. If not, discuss why there is no limit. $$\lim _{x \rightarrow 1} \frac{1}{(x-1)^{3}}$$

What does it mean to say the limit of \(f(x),\) as \(x\) approaches \(c,\) is undefined?

The position function \(s(t)=-16 t^{2}+144 t\) gives the position of a projition of a projectile as a function of time. Find the average velocity (average rate of change) on the interval \([1,2] .\)

For the following exercises, determine where the given function \(f(x)\) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. $$f(x)=\frac{x^{2}-2 x}{x^{2}-4 x+4}$$

For the following exercises, evaluate each limit using algebraic techniques. $$\lim _{h \rightarrow 0}\left(\frac{\sqrt{h^{2}+25}-5}{h^{2}}\right)$$