Free Printable Limits (infinite limits, limits at infinity & continuity)

1.

Evaluate the limit.

a)

$\infty$

b)

$-\infty$

c)

11

d)

DNE

2.

Evaluate the limit.

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

3.

Evaluate the limit.

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

4.

What is the limit as x approaches 2?

a)

0

b)

4

c)

$\frac{1}{4}$

d)

DNE

5.

What is the limit as -2 from the left?

a)

$\infty$

b)

$-\infty$

c)

0

d)

$-\frac{1}{4}$

6.

Identify the vertical asymptote(s) in the function above. (Hint: The last three problems used this same function.)

a)

$x=2$

b)

$x=\pm2$

c)

$x=-2$

d)

There are no vertical asymptotes.

7.

What is the limit of the function?

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

8.

What is the limit of the function?

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

9.

What is the limit of the function?

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

10.

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

11.

Evaluate the limit.

a)

$\infty$

b)

$-\infty$

c)

0

d)

5

12.

Evaluate the limit.

a)

$\infty$

b)

$-\infty$

c)

0

d)

5

13.

Identify the horizontal asymptote(s). (Hint: The last two question used the same function.)

a)

$y=5$

b)

$y=-5$

c)

$y=\pm5$

d)

There are no horizontal asymptotes.

14.

Identify the discontinuities in the function.

a)

$x=1,\ 2,\ 3,\ 4,\ 5,\ 6$

b)

$x=2,\ 3,\ 4,\ 5,\ 6$

c)

$x=2,\ 3,\ 4,\ 5$

d)

$x=2,\ 3,\ 4$

15.

Which discontinuities violate the first condition? Condition 1: f(a) is defined (a is in the domain of f).

a)

$x=3$

b)

$x=2,\ 3$

c)

$x=2,\ 3,\ 4$

d)

$x=2,\ 4$

16.

Which discontinuities violate the second condition? (Condition 2: The limit as x approaches a exists.)

a)

$x=2,\ 3$

b)

$x=2,\ 3,\ 4$

c)

$x=2,\ 4$

d)

$x=3,\ 4$

17.

Which discontinuities violate the third condition? (Condition 3: The value of f equals the limit of f at a.)

a)

$x=2,\ 3,\ 4$

b)

$x=2,\ 3$

c)

$x=3,\ 4$

d)

$x=2,\ 4$

18.

For which values is the function below continuous?
$f\left(x\right)=2x^3+x+2$

a)

It is continuous on [−1,0], but not for all x.

b)

It is continuous for some x, but not on [−1,0].

c)

It is continuous for all x.

d)

It is not continuous on any interval.

19.

$f\left(x\right)=2x^3+x+2;\ \left(-1,\ 0\right)$

What is the value at the left endpoint?

a)

2

b)

-1

c)

0

d)

1

20.

$f\left(x\right)=2x^3+x+2;\ \left(-1,\ 0\right)$
What is the value at the right endpoint?

a)

-1

b)

0

c)

1

d)

2

21.

Can the Intermediate Value Theorem be used to show that f(x) has a solution on (-1, 0)? (Hint: The last two questions can be used to help answer this.)
$f\left(x\right)=2x^3+x+2$

a)

It can be used because the function is defined on (−1,0) and 0<f(−1)<f(0).

b)

It can be used because the function is continuous on [−1,0] and the function is defined at x=−1 and x=0.

c)

It can be used because the function is defined on (−1,0) and f(−1)<f(0)<0.

d)

It can be used because the function is continuous on [−1,0] and 0 is between f(−1) and f(0).

22.

$f\left(x\right)=2x^3+x+2$

There is/are a solution(s) to the equation in (−1,0) at

a)

$x\approx2.235$

b)

$x\approx-0.835$

c)

$x\approx-0.835,\ 2.235$

d)

There is not a solution in (-1, 0)

Limits (infinite limits, limits at infinity & continuity)

Total questions: 22

Worksheet time: 2hrs 50mins

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