Limit Theorems

Using the same graph and given the previous 2 answers, what is  $\lim_{x\rightarrow2}\ f\left(x\right)$ ?

(a)  

Given the graph of f(x), what is  $\lim_{x\rightarrow2^-}\ f\left(x\right)$  ?

(a)  

Evaluate $\lim_{y\rightarrow-2}\ \ \frac{4-3y^2-y^3}{6-y-y^2}=$   

(a)  

lim_x→2 f(x)=

• 3

• 2

• 0

• 1.7

What is the

 $\lim_{x\rightarrow-2}\frac{x³+5x²}{x²}$  ?

• 3

• 7

• -12

• -3

Determine $\lim_{x\rightarrow4}\left(\sqrt{x-3}\right)$  using limit theorems.

• -1

• 0

• 1

•  $\pm1$  
  

• -5

• -4

• -3

• -2

Given the function f(x) , Prove if it is continuous or discontinuous on 1.

Due to the previous 3 problems, is the function continuous on 1?

• yes

• no

Compare $f\left(-2\right)\ and\ \lim it\ as\ x\rightarrow-2$ 

•  $f\left(-2\right)=0=\lim_{x\rightarrow-2}f\left(x\right)$  
  

•  $f\left(-2\right)=0\ne\lim_{x\rightarrow-2}f\left(x\right)$  

•  $f\left(-2\right)=-1=\lim_{x\rightarrow-2}f\left(x\right)$  
  

•  $f\left(-2\right)=-1\ne\lim_{x\rightarrow-2}f\left(x\right)$  
  

Find the limit as x approaches 3 from the left

• 4
• 3
• 2
• DNE