AP Calculus Limits and Continuity Review

Given that $$\lim_{x\rightarrow2}f\left(x\right)=7\ and\ \lim_{x\rightarrow2}\ g\left(x\right)=9,$$  find  $$\lim_{x\rightarrow2}\frac{f\left(x\right)}{\text{g(x)}}.$$  

Find  $$\lim_{x\rightarrow0}\frac{x^2-4x+8}{x-2}$$ . 

What is the $$\lim_{x\rightarrow-5}\ \frac{x^2-25}{x+5}$$  ?

Determine whether $$f\left(x\right)=\frac{x^2+5x-6}{x-1}$$   is continuous or discontinuous at $$x=1.$$  

A function $$f\left(x\right)$$  has to be continuous at $$x=a$$  if the $$\lim_{x\rightarrow a}\ f\left(x\right)$$  exists.

If $$\lim_{x\rightarrow a}\ f\left(x\right)\$$  does not exist, then $$f\left(x\right)$$  is undefined at the point $$x=a.$$  

Determine whether the function f(x) is continuous or discontinuous at $$x=2.$$  

Consider the graph of f(x). What is the $$\lim_{x\rightarrow2^-}\ f\left(x\right)?$$  

Evaluate $$\lim_{x\rightarrow\infty}\ \frac{4x^3-8x^2+11}{5x^3+3x-9}$$  

Evaluate $$\lim_{x\rightarrow0}\ \frac{4\ \sin3x}{2\ \tan5x}$$