Limits of Piecewise Functions and Limits at Infinity

What is the limit of h(x) as x approaches -4?

• $16$

• $4$

• $-4$

• $DNE$

What is the limit of g(x) as x approaches -3?

• $-\frac{1}{3}$

• $\frac{1}{3}$

• $-3$

• $DNE$

Check all the boxes that contain true statements.

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

• $\lim_{x\rightarrow-2}\ \ g\left(x\right)\ =e^{-2}$

• $\lim_{x\rightarrow0^-}\ \ g\left(x\right)=1$

• $\lim_{x\rightarrow0}\ \ g\left(x\right)=1$

 $\lim_{x\rightarrow+\infty}\ \ f\left(x\right)=?$  

Check all the boxes that contain true statements.

• $\lim_{x\rightarrow-\infty}\ f\left(x\right)=0$

• $\lim_{x\rightarrow-\infty}\ f\left(x\right)=-\infty$

• $\lim_{x\rightarrow+\infty\ }f\left(x\right)=3$

• $\lim_{x\rightarrow+\infty}\ f\left(x\right)=+\infty$

 $\lim_{x\rightarrow+\infty}\ f\left(x\right)=?$  

•  $0$  

•  $-\infty$  

•  $+\infty$  

•  $DNE$  

 $\lim_{x\rightarrow-\infty}\ \frac{4}{3x^3}=$  

•  $0$  

•  $+\infty$  

•  $-\infty$  

•  $DNE$  

If f(x) is a rational function and y = b is its horizontal asymptote, then what is $\lim_{x\rightarrow+\infty}\ f\left(x\right)?$  

•  $b$  

•  $-b$  

•  $+\infty$  

•  $-\infty$  

 $\lim_{x\rightarrow-\infty}\frac{3x^2+2x^3+x-7}{x^3-3x+5}=$  

 $\lim_{x\rightarrow+\infty}\frac{5x^4-3x^3+9}{4x^4-2x^2+x-1}=\$  

•  $0$  

•  $\frac{5}{4}$  

•  $+\infty$  

•  $DNE$