1. Limits

2. a limit is the value that a function or sequence "approaches" as the input approaches some value.

3. Fill in the blank…. You can always make a ___________ turn on red unless a sign is posted prohibiting it.

4. Give me liberty or ___________ me death!

5. Don’t cry over spilled ____________.

6. xf(x) 03 13 2Undefined 33 43

8. Let the graph below represent the function f(x)

11. Two important ideas about limits: The limit of a function at a point is the logical y-value at that point. We do not care what the value of a function actually is at the point where we’re looking for the limit.

13. Find the

14. Find

15. Try on your own by sketching a graph Find 1) 2) 3)

20. Three types of discontinuity Removable discontinuity – When the graph is continuous except for a hole. Jump discontinuity – When the left and right side limits are different. Infinite discontinuity – Created by vertical asymptotes.

21. Limits and Infinity Cheat code: Divide each term by x of the highest degree in the function.

22. The graph f(x) has, at most, one horizontal asymptote. – If the degree of the numerator (p(x)) is less than the degree of the denominator (q(x)), then the line y = 0 (the x-axis) is a horizontal asymptote. – If the degree of p(x) is equal to the degree of q(x), then the line y = a/b, where a is the leading coefficient of p(x) an b is the leading coefficient of q(x). – If the degree of p(x) > degree of q(x), then there are no horizontal asymptotes.

23. Limits Practice with solutions http://archives.math.utk.edu/visual.calculus/1 /limits.15/