Module 2 - Limits n Shit

Question 1

What do we do if we have both positive and negative infinity as the answer to a limits problem?

Answer 1

We use one-sided limits to further simplify

Question 2

If one-sided limits do not match, what does this mean

Answer 2

the limit is DNE

Question 3

What is the first step to any limits problem?

Answer 3

Insert into the function

Question 4

What are the three types of discontinuities?

Answer 4

1. Junction Point
2. Zero Denominator (usually VA)
3. Single Point Hole

Question 5

What does indeterminite mean?

Answer 5

When a limit is not fully simplified, and a limit can still be found we deem it indeterminate

Question 6

Are undefined and indeterminate the same thing?

Answer 6

No

Question 7

What are all the possible ways we can simplify an indeterminate limit?

Answer 7

-Factoring

-Difference of squares/cubes

-Sum of cubes

-Multiplying by the conjugate (can do so twice)

Question 8

What are the definitions of a LHA and an RHA

Answer 8

Question 9

What are all the possible ways we can simplify an infinite limit? e.i looking for a horizontal asymptote

Answer 9

• Factoring out the highest power when x is approaching infinity (or, where appropriate, deleting the small power terms as a shortcut)
• Using graphical evidence (recall you should only do this if you are making use of graphs which you know everything about without needing to depend on technology, such as y=sin(x) or y=ln(x)).