Limits

3. If f is continuous on the closed interval [a,b], f(a) does not equal f(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.
6. Touches the function at two points. You can use precalculus to find it.
7. Using a picture to solve the limit.
9. You find these by seeing where x approaches from either side. We use "L" when writing the answer.
13. Touches the function at one point. Equivalent to finding the slope.
14. When f cannot be redefined to make it continuous.
16. _______ either the numerator or denominator of a fractional expression.
17. The limit of any constant is the ________.
18. If p is a ______ function and c is a real number, then the limit is equal to p(c).
20. When the limit of a function is sandwiched between two other functions, each of which has the same limit at a given x-value.
22. The mathematics of change. Mathematics of velocities, accelerations, tangent lines, etc.
24. Plugging in the limit to get the answer.

1. ______ theorems tell you something but do not provide a method for finding it.
2. The limit from the left does not equal the limit from the right. Increases or decreases without bound.
4. Using a table to solve the limit.
5. _____ hand limit is the answer from the left side of the function. We use a - after the number the limit is approaching to write it symbolically.
8. When f can be made continuous by redefining the function.
10. When a function is defined but not continuous.
11. Finding common factors and canceling them.
12. The limit as x approaches 0 of (1-cos(x))/x is equal to ____.
15. If r is a _____ function given by r(x)=p(x)/q(x) and c is a real number such that q(c) cannot equal 0, then the limit is equal to r(c).
19. The limit as x approaches 0 of sin(x)/x is equal to ____.
21. A number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point.
23. When these conditions are met: 1. f(c) is defined. 2. The limit exists. 3. The limit as x approaches c is equal to f(c).