1.5 Infinite Limits and Limits at Infinity

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

• ³/₇

• 0

• $\infty$

• $-\infty$
  

Tags

CCSS.HSF-IF.C.7D

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

• ^-2/₉

• 0

• $\infty$

• $-\infty$

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.B.3

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

• 0

• DNE

• 1/2

• 2

Tags

CCSS.HSF-IF.C.8B

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

•  $\infty$  

•  $-\infty$  

• 2

• 2/3

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

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

•  $\infty$  

•  $-\infty$  

• 2

• 3

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

•  $\infty$  

•  $-\infty$  

• 0

• DNE

Tags

CCSS.HSF-IF.C.7E

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

Tags

CCSS.HSF-IF.C.7D

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

• 1

• 0

• DNE

• 4

Tags

CCSS.HSF.LE.A.3

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

• DNE

• 1

• 0

•  $-\infty$  

Find the limit

• ⁶/₅

• 0

• $\infty$

• $-\infty$
  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

CCSS.HSF.LE.A.3