Semester 1 Final Review

Question 1

lim [x->0] sin(x)/x

Answer 1

1

Question 2

Strategies for finding Limits

Answer 2

1) plug the number in

2) if “0/0”
- factor
- expand
- conjugate
- common denominator

3) graphing calculator (table of values)

Question 3

lim [x->0] (1-cos(x))/x

Answer 3

0

Question 4

Definition of Continuity

Answer 4

A function f is continuous at c if the following three conditions are met.

1) f(c) is defined.
2) lim [x->c] f(x) exists.
3) lim [x->c] f(x) = f(c)

Question 5

The Intermediate Value Theorem

Answer 5

If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c)=k.