1. Quiz 7-3 to 7-5
Trig Integrals
Trig Substitution (notecard)
Partial Fractions

2. True/False
1) A limit describes how a function moves as x moves toward a certain point.
2) A limit is a number or point past which a function cannot go.
3) A limit is a number that the y-values of a function can be made arbitrarily close to by restricting x-values.

3. True/False
4) A limit is a number or point the functions gets close to but never reaches.
5) A limit is an approximation that can be made as accurate as you wish.
6) A limit is the value reached by plugging in numbers closer and closer to a given number.

4. Indeterminate Forms and L’Hopital’s Rule
Section 7.7 AP Calc

5. Find the limit:

6. Thm 7.3 Extended Mean Value Theorem
If f and g are differentiable on an open interval (a,b) and continuous on [a,b] such that g’(x)≠0 for any x in (a,b), then there exists a point c in (a,b) such that

7. Thm 7.4 L’Hopital’s Rule
Let f and g be functions that are differentiable on an open interval (a,b) containing c, except possibly at c itself. Assume g’(x)≠0 for all x in (a,b), except possibly at c itself. If the limit of f(x)/g(x) as x approaches c produces the indeterminate form 0/0, then

8. provided the limit on the right exists (or is infinite)
provided the limit on the right exists (or is infinite). This result also applies if the limit of f(x)/g(x) as a approaches c produces any one of the indeterminate forms ∞/∞,
(- ∞)/ ∞, ∞/(- ∞), or (- ∞)/(- ∞).

9. Determine the limits: A) B)

10. C) D)

11. Other indeterminate forms:

12. Find the limit: E)

13. F) G)

14. Use Graphing Calculator to check limits
Notice: