Infinite Limits

Select all statements that are TRUE.

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

•  $-\infty$  

•  $\infty$  

•  $\frac{1}{2}$  

• 0

•  $-\frac{1}{2}$ 

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.

• DNE

• Postive infinity

• Indeterminate

• Negative infinity

Determine the value of the limit

• ∞

• -∞

• DNE

• 0

• Does not exist

• Positive infinity

• Negative infinity

• Undefined

Evaluate

 $\lim_{x\rightarrow-2^+}\left(\frac{4x}{x^4-16}\right)$  

•  $+\infty$  

•  $-\infty$  

•  $undefined$  

•  $0$  

• Negative infinity

• Undefined

• Potive infinity

• Does not exist

• Positive infinity

• -2

• Negative infinity

• DNE

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

•  $\infty$  

•  $-\infty$  

• 2

• 2/3