Limits and Continuity

Question 1

lim sin (Ө)/Ө,x,0

Answer 1

1

Question 2

Conditions for Continuity

Answer 2

lim f(x),x,a exists
f(a) exists
lim f(x),x,a = f(a)

Question 3

Conditions for Limit laws

Answer 3

• Limits have to approach the same number

- Limits have to exist and be finite

Question 4

Horizontal Asymptotes, P(x)/Q(x)

Answer 4

P>Q, lim=∞, -∞
P=Q, a/b, where a and b are leading coefficients
P<Q, lim=0

Question 5

Proving a Limit Exists

Answer 5

If the limit from the right and the limit from the left equal eachother

Question 6

lim (1+1/n)^n,n,∞

Answer 6

e