Math 125 Test 3 4 pts each March 8, 2007

(4 points absolutely free!)

Graph

1. y = 4^x

2. y = (3/4)^x

3. y = (9/4) ^x

4. y = e^x

5. y = 3^{- x}

6. y = log₆ x

7. y = ln x

8. y = log_1/2 x

Evaluate:

9. log₃ 81

10. log₁₆ 4

11. log_1/2 8

12. log₁₂₅ x = 2/3

13. log₇1

14. log₄0 =

15. log₈ 8=

16. ln e

17. ln e²

18. Find the equation of the line tangent to at x = 5 .

Find the differential df for :

19. f(x) = sin (x²)

20. f(x) = e^3x

21. f(x) = 5^x/2

22.

23. f(x) = x² sin²x

24. The height of a right triangle remains fixed at 6 m while the base expand at a constant rate of 5 m/s. How fast is the hypotenuse increasing when the base is 8 m?

5 pts bonus

A 20 ft ladder leaning against a wall is sliding down the wall so that the the bottom is moving away from the wall 5 ft/s . How fast is the top moving down the wall at the instant the bottom is 16 ft from the wall ?