AP Calculus AB Chapter 2 Review

$$\lim_{x\rightarrow0}\frac{5x^4+8x^2}{3x^4-16x^2}=$$  

(a)  

Circle all x-values where the graph has a limit, but is not continuous.

$$f\left(x\right)=\left\{\frac{x-1}{x^2-4},\ \ x<1\right\}\ and\ f\left(x\right)=\left\{-3,\ \ x\ge1\right\}$$  

For the piecewise function above, which statement is true?

$$\lim_{x\rightarrow-1}\frac{2x^2-x-3}{x+1}=$$  

(a)  

Calculate the average rate of change of $$y=\cos\left(\pi x\right)$$  from x=0 to x=1/3.

(a)  

For the graph of $$y=j\left(x\right)$$  , which statement below is false?

$$\lim_{x\rightarrow0}\frac{5\tan4x}{2x}=$$  

(a)  

$$\lim_{x\rightarrow-1-}\frac{\left|3x+5\right|}{x+1}$$  

For $$g\left(x\right)=4+3^{\left(2-x\right)}$$ , determine $$\lim_{x\rightarrow\infty}g\left(x\right)$$ .

(a)