Limits

1. Touches the function at two points. You can use precalculus to find it.
5. When the limit of a function is sandwiched between two other functions, each of which has the same limit at a given x-value.
7. Plugging in the limit to get the answer.
10. The limit of any constant is the ________.
14. 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.
15. Using a picture to solve the limit.
16. 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).
17. The limit as x approaches 0 of (1-cos(x))/x is equal to ____.
18. _______ either the numerator or denominator of a fractional expression.
19. When a function is defined but not continuous.
21. If p is a ______ function and c is a real number, then the limit is equal to p(c).
22. The limit as x approaches 0 of sin(x)/x is equal to ____.
23. You find these by seeing where x approaches from either side. We use "L" when writing the answer.
24. When f can be made continuous by redefining the function.
26. The limit from the left does not equal the limit from the right. Increases or decreases without bound.

2. Touches the function at one point. Equivalent to finding the slope.
3. 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).
4. Finding common factors and canceling them.
6. ______ theorems tell you something but do not provide a method for finding it.
8. Using a table to solve the limit.
9. The mathematics of change. Mathematics of velocities, accelerations, tangent lines, etc.
11. A number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point.
12. When f cannot be redefined to make it continuous.
13. If f(x) approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line x = c is a _________ of the graph of f.
20. ____ limits decrease or increase without bound as x approaches c.
25. _____ 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.