Recap Limits

• 13
• 7
• 6
• -3

What technique would you use to find this limit?

• Direct Substitution only

• Factor & Cancel

• Conjugate Multiplication

• Rewrite with a Trig Identity

• DNE
• -10
• -3
• -4

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

If the limit does not exist, write "DNE."

 $f\left(4\right)=$  

If the function value is undefined, write "UND."

 $\lim_{x\rightarrow2}f\left(x\right)=$  

If the limit does not exist, write "DNE."

Mathematical Equivalence

ON

1. Which of the following statements about limits is false?

• The two broad areas of calculus known as differential and integral calculus are built on the foundation concept of a limit.

• $x\rightarrow1^-$ indicates that x approaches 1 from the right.

• If the $\lim_{x\rightarrow a^{-\ }}f\left(x\right)$ is different from the $\lim_{x\rightarrow a^{+\ }}f\left(x\right)$ , then the $\lim_{x\rightarrow a}\ f\left(x\right)$ does not exist.

• The limit of x when x is approaching a is a. $\lim_{x\rightarrow a}x\ =\ a$

Use the theorems to evaluate the limit  $\lim_{x\rightarrow-3}\ \frac{\left(2x\ +6\right)}{4x^{2\ }-36}$  

• 0

• does not exist

•  $-\frac{1}{12}$  

• -1

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

• -1

• 2

• undefined

• 1