Review Practice on Limits

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

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

Find the limit

• ⁶/₅

• 0

• $\infty$

• $-\infty$
  

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

• 0

• -1

• -5

•  $\infty$   

•  $-\infty$  

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

• - 4

• - 2

• 1

• 2

•  $\infty$  

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

•  $-\infty$  

•  $\infty$  

•  $\frac{1}{2}$  

• 0

•  $-\frac{1}{2}$ 

 $The\ \lim_{x\rightarrow0}f\left(x\right)\$  fails to exist because...

• As the function approaches zero, left and right of zero do not match

• As the function approaches zero, the graph oscillates.

• As the function approaches zero, the graph increases without bound.

• The function only approaches zero from one side.

• 0

• 1/4

• 1

• $\infty$