Calculus 10 WW # 2

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

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

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

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

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

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

Evaluate the limit.