Limits and Continuity

1. Limits and Continuity 1.2

2. Continuity at a point • A function is continuous at any point given three things • 1. The function exists • 2. The limit as x approaches that point exists • 3. The function = the limit at that point

3. Continuous from the right/left • All of the same rules apply, but we only check the one sided limit in question

4. Example • Is the given function continuous at x=1? • X=4? • X=5? • Why not?

5. Continuity on an interval • To be continuous on an interval means that the function is continuous at every point on that interval.

6. Continuity on an interval • The following types of functions are continuous everywhere on their domain: • Polynomials, rational functions, root functions, trig functions, exponential functions, and logarithmic functions

7. Continuity rules • If f and g are continuous functions • f + g is continuous • f - g is continuous • f x g is continuous • f / g is continuous where g ≠ 0 • f(g) is continuous

8. Example • Where are each of the following functions discontinuous

9. Example

10. Homework • Pg121 #27-31 tell me why, 43-49