Limits & Continuity Review

$$\lim_{x\rightarrow\infty}\ \frac{3x^2-5x+8}{2x-7}$$  

$$\lim_{x\rightarrow\infty}\ \frac{4x-2x^2+3}{7+e^x}$$  

$$\lim_{x\rightarrow\ -\infty}\ \frac{e^x}{x^4}$$  

What is/are the horizontal asymptotes for $$f\left(x\right)=\frac{\sqrt[]{9x^6-7x+2}}{2x^3-1}$$  

What is/are the horizontal asymptotes of $$f\left(x\right)=\frac{\sqrt[]{3x^4-2}}{7x^{ }+x^2}$$  

What is/are the horizontal asymptotes of $$f\left(x\right)=\frac{\sqrt[]{4x^{10}-5x^7-2}}{3x-2x^5}$$  

Identify the type of discontinuity and the x-value where it occurs:

$$f\left(x\right)=\frac{x^2-3x-10}{x^2+x-30}$$  

Is f(x) continuous at x= -2?

If $$f\left(x\right)=x^3-6x+2$$  , does the IVT guarantee that there exists a point c between x=-1 and x=2 such that f(c)=0?

$$\lim_{x\rightarrow0}\ x^2\sin\left(\frac{1}{x^3}\right)$$    (Hint: Squeeze Theorem)