limits at infinity

Find the limit. Hint: Where is the horizontal asymptote?

Find the limit. Hint: Where is the horizontal asymptote?

$$\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}$$  

$$\lim_{x\rightarrow\infty}\left(2x^3+3x-1\right)=$$  
Hint:  Think of the end behavior

$$\lim_{x\rightarrow-\infty}\left(x^2+3x-1\right)=$$  
Hint:  Think of the end behavior of an even and positive polynomial.

$$\lim_{x\rightarrow\infty}e^x=$$  
Hint:  Think of the end behavior

Determine the limit at infinity by finding the slant asymptote using long division and then looking at the end behavior of the slant asymptote.
$$\lim_{x\rightarrow\infty}\left(\frac{x^2-x-12}{x+3}\right)$$  

Find the limit

$$\lim_{x\rightarrow\infty}\ \frac{x^3-x^2+1}{5-3x-x^4}=...$$  

$$\lim_{x\rightarrow\infty}\ \frac{x+7}{\sqrt{4x^2+3x}}=...$$