Limits at Infinity

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

• ³/₇

• 0

• ∞

• -∞

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

• ^-2/₉

• 0

• ∞

• -∞

 $\lim_{x\rightarrow\infty}\left(\frac{5}{x^2+1}\right)$  = 
Hint:  Where is the horizontal asymptote?

(a)  

Tags

CCSS.HSF-IF.C.8B

 $\lim_{x\rightarrow\infty}\left(\frac{4x}{x+3}\right)$  = 

(a)  

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

•  $\infty$  

•  $-\infty$  

• 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

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

•  $\infty$  

•  $-\infty$  

• x

• e

Tags

CCSS.HSF-IF.C.7E

Think about the slope of the slant asymptote for the equation  $f\left(x\right)=\frac{x^2-x-12}{x+3}$  .  Is the slope positive or negative?   Graph in Desmos to check.  

• negative

• positive

Tags

CCSS.HSF-IF.C.7D

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

Find the limit

• ⁹/₁₂

• 0

• ∞

• -∞