Lesson 1 Limits & Continuity

Question 1

Lim𝑓(𝑥) = 𝐿
𝑥→𝑎−

Answer 1

The limit of f(x) as a x approaches a from the left, equals L

Question 2

Lim𝑓(𝑥) = 𝐿
𝑥→𝑎+

Answer 2

The limit of f(x) as a x approaches a from the right, equals L

Question 3

So, if Lim 𝑓(𝑥) ≠ Lim 𝑓(𝑥)
𝑥→𝑎− 𝑥→𝑎+

Answer 3

Then Lim𝑓(𝑥) does not exist
𝑥→𝑎

Question 4

What is domain?

Answer 4

Set of all input values of a function

Question 5

The denominator can’t be?

Answer 5

zero

Question 6

If the limit is of the form nonzero/zero

Answer 6

The limit does not exist

Question 7

If the limit has the form 0/0

Answer 7

Then factor, simplify, rationalize, until a IS in the domain

Question 8

If we cannot change f(x) so that a is in the domain

Answer 8

The limit does not exist

Question 9

What’s a removable discontinuity?

Answer 9

When there is an open whole in the graph

Question 10

What’s a jump discontinuity?

Answer 10

When there is a discontinued graph and a new one

Question 11

What’s an infinite discontinuity?

Answer 11

When there are two graphs or one that doesn’t have a estimated end point

Question 12

If you can cancel a factor from a rational function, then…

Answer 12

There is a hole at the zero of that factor

Question 13

There is vertical asymptote at the zeros of the factors that…

Answer 13

Remain in the denominator after canceling