1. Miss Battaglia AP Calculus

2. The natural logarithmic function is defined by The domain of the natural logarithmic function is the set of all positive real numbers.

3. The natural log function has the following properties. 1. The domain is (0,∞) and the range is (-∞, ∞) 2. The function is continuous, increasing, and one-to-one 3. The graph is concave down.

4. If a and b are positive numbers and n is rational, then the following properties are true. 1. ln(1) = 0 2. ln(ab) = ln a + ln b 3. ln(a n ) = n ln a 4. ln(a/b) = ln a – ln b

5. a.b.

6. c.d.

7. The letter e denotes the positive real number such that

8. a. ln 2 b. ln 32 c. ln 0.1

9. Let u be a differentiable function of x. 1. 2.

10. a.b.

11. c.d.

12. Differentiate

14. Find the derivative of

15. If u is a differentiable function of x such that u≠0, then

16. Find the derivative of

17. Locate the relative extrema of

18. BC: Read 5.1 Page 331 #11-17 odd, 47-61 odd, 83, 91, 101, 102