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.HSF-IF.C.8B

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.HSF-IF.C.8B

 $\lim_{x\rightarrow\infty}\left(2x^3+3x-1\right)=$  
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

 $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.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

 $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.

Tags

CCSS.HSF-IF.C.7A

 $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.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

 $The\ \lim_{x\rightarrow2}f\left(x\right)\$  fails to exist because...

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

• As the function approaches two, the graph oscillates.

• As the function approaches two, the graph increases or decreases without bound.

Tags

CCSS.HSF-IF.C.7A