2.5 Limits at Infinity

2.5 Limits at Infinity

End Behavior of Functions

Fill in the Blanks

If the graph of f(x) approaches the horizontal line y = b as $x\rightarrow\infty$  , the line y = b is called a 

Multiple Choice

 $\lim_{x\rightarrow\pm\infty}\left(\frac{1}{x^n}\right)=$  

•  $\pm\infty$  

•  $\pm1$  

•  $0$  

•  $\pm\frac{1}{2}$  

Multiple Choice

 $\lim_{x\rightarrow\infty}\left(\frac{x}{2x+1}\right)$  

• 1/2

• 1

•  $\infty$  

• 2

Multiple Choice

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

• 2/3

• 1/2

• 1

•  $\infty$  

Multiple Choice

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

• 1

• 1/2

•  $\infty$  

• 0

Multiple Choice

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

• 1

• 1/2

•  $-\infty$  

•  $\infty$  

Multiple Choice

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

•  $\infty$  

•  $-\infty$  

• 0

• 1

Multiple Choice

 $\lim_{y\rightarrow\infty}\left(\frac{2y^2+y-5}{4y^2+5y+2}\right)$  

• 1/2

•  $\infty$  

• 2

• -1