Limits Continued

Question 1

Intermediate Value Theorem

Answer 1

For any value of f that is continuous over [a,b]. There exists a point c for which f(c)=L

Question 2

Continuity Checklist

Answer 2

1) Is f(a) defined
2) Does the limit of f(x) exist?
3) Does f(a) = lim of f(x)

Question 3

Which functions are continuous on their domains? (list 4)

Answer 3

1) Polynomials
2) Rational Functions
3) Trig Functions
4) Root Functions

Question 4

What are the four types of discontinuities?

Answer 4

1) Removable Discontinuity (hole) Limit exists but the point does not exist.
2) Jump Discontinuity (two limits give two different answers)
3) Oscilating Discontinuity (cannot determine what the limit is approaching nor the value of th epoint)
4) Infinite Discontinuity. (approaching infinity or negative infinity for the limit. Point is not defined.