Free Printable Limit Theorems

1.

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

(a)

2.

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

(a)

3.

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

(a)

4.

lim_x→2f(x)=

a)

3

b)

2

c)

0

d)

1.7

5.

What is the

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

?

a)

3

b)

7

c)

-12

d)

-3

6.

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

a)

-1

b)

0

c)

1

d)

$\pm1$

7.

Determine $\lim_{x\rightarrow-2}\left(x-2\right)$ using table of values.

a)

-5

b)

-4

c)

-3

d)

-2

8.

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?

a)

yes

b)

no

9.

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

a)

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

b)

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

c)

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

d)

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

10.

Find the limit as x approaches 3 from the left

a)

4

b)

3

c)

2

d)

DNE

11.

The table above gives values of a function $f$ at selected values of $x.$ Which of the following conclusions is supported by the data in the table?

a)

$\lim_{x\rightarrow2}f\left(x\right)=-1$

b)

$\lim_{x\rightarrow2}f\left(x\right)=6$

c)

$\lim_{x\rightarrow2^-}f\left(x\right)\ =-1$ and $\lim_{x\rightarrow2^+}f\left(x\right)=6$

d)

$\lim_{x\rightarrow2^-}f\left(x\right)=6$ and $\lim_{x\rightarrow2^+}f\left(x\right)=-1$

12.

Evaluate $\lim_{x\rightarrow4}\ \sqrt{x^2+4x+4}$ ?

a)

36

b)

6

c)

-36

d)

-6

13.

Evaluate

\lim_{x\rightarrow5^+}\left(\frac{4}{x-5}\times\frac{1}{2x}\right)

a)

$undefined$

b)

$+\infty$

c)

$0$

d)

$-\infty$

14.

Using Limit Theorems, which of the following is the $\lim_{x\rightarrow1}\left(\frac{3x-2}{x^2-5x+10}\right)$ ?

a)

1/6

b)

1/5

c)

1/4

d)

1/3

15.

What is the

\lim_{x\rightarrow5}\frac{x²-10}{5}

?

a)

0

b)

-1

c)

3

d)

7

Limit Theorems

Total questions: 15

Worksheet time: 15mins

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