Limits

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. $\lim_{x\rightarrow a}x\ =\ a$

Given the graph for f(x), what is the  $\lim_{x\rightarrow1}f\left(x\right)$  ?

• -1

• 0

• 3

• 4

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

(a)  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Using the same graph, what is  $\lim_{x\rightarrow2^{+\ }}f\left(x\right)$  ?

(a)  

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

(a)  

Tags

CCSS.HSA.REI.D.10

Use the theorems to evaluate the limit  $\lim_{x\rightarrow-2}\ \frac{2}{4-x}$  

•  $\frac{1}{3}$  

•  $-\frac{1}{3}$  

• 1

• -1

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

Given the function f(x) , Prove if it is continuous or discontinuous on 1.
b.  $\lim_{x\rightarrow a}\ f\left(x\right)$  = ?

• 2

• -1

• 1

• does not exist

Given the function f(x) , Prove if it is continuous or discontinuous on 1.
c.  $f\left(a\right)\ =\ \lim_{x\rightarrow a}\ f\left(x\right)$  ?

• yes

• no