Limit Notation

Name:

Class:

Date:

Show your work for each problem.

1.
How do you read ?
1. a) equals in
2. b)The function equals
3. c)The limit of as approaches
4. d)The value of
2.
What does the arrow () mean in limit notation?
1. a)Transforms into
2. b)Is greater than
3. c)Approaches (gets arbitrarily close to)
4. d)Equals
3.
In the expression , what value is approaching?
4.
What does mean?
1. a)The limit as approaches from the right
2. b) equals plus something
3. c)The limit as approaches from the left
4. d)The limit as approaches positive
5.
If , what is ?
6.
What does represent?
1. a)The left-hand limit at
2. b)The negative limit at
3. c)The limit of
4. d)The right-hand limit at
7.
Write the limit notation for: "The limit of as approaches equals ."
8.
What does mean?
1. a)When ,
2. b)The function has a maximum value of
3. c)As grows without bound, approaches
4. d) grows to infinity at
9.
In , from which direction does approach ?
10.
Translate to limit notation: "As approaches from the left, approaches ."
11.
What does it mean if ?
1. a)The function is continuous at
2. b)The function equals at
3. c)The two-sided limit does not exist
4. d)The one-sided limits are both infinite
12.
Interpret the statement:
13.
Which statement correctly interprets ?
1. a)The sine of divided by equals
2. b)When , the function equals
3. c)
4. d)As approaches , the ratio approaches
14.
If and , what is ?
15.
Write the complete limit notation for: "As time increases without bound, the population approaches its carrying capacity of ."
16.
What is wrong with writing just ""?
1. a)It doesn't specify what value approaches
2. b)The function name should be in parentheses
3. c)The equal sign is not needed
4. d)The limit value should be written first