Limits at Infinity

Which of the following actions are appropriate for finding a limit at infinity? Look for multiple answers.

• If the function is polynomial, look at rules for end behavior.

• If the function has a HA, that will determine the limit at infinity.

• If the function has a slant asymptote, look at the end behavior of that line (the slant asymptote)

• Look at the function graphically to determine end behavior.

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

• ³/₇

• 0

• ∞

• -∞

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

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

• ^-2/₉

• 0

• ∞

• -∞

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• 0

• DNE

• 1/2

• 2

Tags

CCSS.HSA.APR.D.7

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

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

Tags

CCSS.HSA.APR.D.7

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

•  $\infty$  

•  $-\infty$  

• 2

• 2/3

Tags

CCSS.HSA.APR.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 of an exponential function.

•  $\infty$  

•  $-\infty$  

• x

• e

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.3

Which statement is true about slant asymptotes?

• Slant asymptotes can be a vertical or horizontal line graphically.

• Slant asymptotes are oblique (not purely vertical or horizontal) lines graphically.

• Slant asymptotes occur when the degree of the denominator is greater.

• Slant asymptotes occur when the degree of the numerator and denominator are equal.

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7