Comp book: Limits

Question 1

3 times a limit DNE

Answer 1

1. Lim doesn’t equal Lim
   X—> c+ X—–> c-
2. When it oscillates
3. Has an asymptote

Question 2

When can a limit be infinite?

Answer 2

When it is one-sided, but a two-sided one can’t be

Question 3

When solving a limit, try to ______ but if that doesn’t work try one of these four:

Answer 3

Direct substitution 
1. Factor
2. Rationalize
3. Common Denominator
4. Trig identities 
   Lim    =  Sinx = 1
X----->0       x

Lim = 1-Cosx = 0
X——>0 x

Question 4

To be continuous…

Answer 4

1. The limit must exist
2. F(a) must exist
3. Limit must equal the point

Question 5

Removable discontinuity

Answer 5

Limit exists but its equal to the point

Question 6

Nonremovable discountinuity

Answer 6

When the limit DNE

Question 7

When you see Lim approaches infinity what should you think? How do you find it?

Answer 7

Horizontal asymptote
Equal - divide
Top bigger than bottom - none
Bottom bigger than the top - 0

Question 8

When it is differentiable you know it is…

What is it not…

Answer 8

A. the function is continuous
B. You can take the derivative

1. Sharp turns
2. Tangent line is vertical
3. Not continuous