infinite limits G12

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

• ³/₇

• 0

• $\infty$

• $-\infty$
  

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

• ^-2/₉

• 0

• $\infty$

• $-\infty$

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

• 0

• DNE

• 1/2

• 2

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

•  $\infty$  

•  $-\infty$  

• 2

• 2/3

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

•  $\infty$  

•  $-\infty$  

• 2

• 3

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

•  $\infty$  

•  $-\infty$  

• -3

• 4

 $\lim_{x\rightarrow\infty}\ \frac{\sin\ x}{x}+4$  

• 1

• 0

• DNE

• 4

 $\lim_{x\rightarrow-\infty}\ \frac{\cos\ x}{x}$  

• DNE

• 1

• 0

•  $-\infty$  

Find the limit

• ⁶/₅

• 0

• $\infty$

• $-\infty$
  

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

• - 4

• - 2

• 1

• 2

•  $\infty$