Limit Theory Short Answers

Question 1

Name 3 things that can go wrong when trying to find a
limit.

Answer 1

Left limit is not the right limit, the values go to an
infinity and the values oscillate.

Question 2

Name the two ways a function can have a limit.

Answer 2

The limit is the value of the function and the function has a removable discontinuity.

Question 3

What don’t limits care about?

Answer 3

The value of the function at the point.

Question 4

Is it possible for both the left and right limits agree but
the limit itself doesn’t?

Answer 4

No

Question 5

Is it possible for both the left and right limits exist but
the limit itself doesn’t?

Answer 5

Yes

Question 6

If I say “if x gets close to 5 then x+2 gets close to 5+2”,
what property of x + 2 am I using?

Answer 6

Continuity

Question 7

How do we symbolically represent the notion “if x gets
close to 5 then 3x gets close to 15”?

Answer 7

lim3𝑥 =15
𝑥→5

Question 8

You can find the limit of a continuous function by doing
this.

Answer 8

Plugging in.

Question 9

What’s the definition of a continuous function?

Answer 9

When you plug in a number, you get the limit.

Question 10

If (x) is continuous, what is the limit of this function
as x goes to 3?

Answer 10

(3)

Question 11

What will our calculator usually do if we try to find the
limit of a discontinuous function by plugging in?

Answer 11

Give us an error.