5.1 to 5.5

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AP Calculus Test: Exponential and Logarithmic Functions (No Calculators)

A. Differentiate with respect to :

1.

2.

3.

4.

5.

6.

7.

8.

B. Evaluate the following integrals:

9.                                                                    13.                                                          

10.                                                           14.

11.                                                              15.

12.                                  16.

17. Evaluate the area bounded by , the axis, the axis, and the vertical line , as shaded in the graph below:

AP Calculus Test: Exponential and Logarithmic Functions (Calculators Permitted)

18. Evaluate .

19. Let be the function given by .

a)      Find the average rate of change of on .

b)      Find the average value of on .

20. Use a trapezoidal sum of four subintervals of equal width to estimate .

21. $700 is deposited into a new savings account at the Hyper Funds Bank . The account is guaranteed a steady interest rate (now you know why it’s called “Hyper Funds”) over the life of the account.

a)      How much money will be in the account after 10 years if interest is compounded on it once per month?

b)      How much money will be in the account after 10 years if interest is compounded on it continuously?

c)      If interest is compounded on the account continuously, after how much time will the account have a balance of $10,000?

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Last modified: 01/09/08