I. FIND THE DERIVATIVE OF EACH FUNCTION.

2 ln(x) 1. f (x)  ln(tan(x)) 2. f (x)  x 3e x 3. f (x)  e x

4. f (x)  e 5x 5. f (x)  ln3 x 2 1 6. f (x)  x 4 ln(x)

II. FIND EACH INDEFINITE INTEGRAL.

1 3 x  4 7. dx 8. x 2e x 4 dx 9. dx  x  3   x 2  8x 1

sec 2 (x) e x e3x 10. dx 11. dx 12. dx  3x 1 tan(x)  x  3  e

III. FIND y USING LOGARITHMIC DIFFERENTIATION. 3 2 x 13. y  x  3x 5 14. y  3 x  3 IIII. FOR THE REMAINING PROBLEMS, YOU NEED ONLY SET UP AN INTEGRAL USED TO COMPUTE THE DESIRED QUANTITY. YOU NEED NOT COMPUTE THE INTEGRAL.

15. FIND THE VOLUME OF THE SOLID DETERMINED BY REVOLVING ABOUT THE Y-AXIS THE REGION BOUNDED BY THE CURVES y  x 2 , y  9 , and x  2 . USE THE WASHER METHOD FOR THIS PROBLEM.

16. USE THE SHELL METHOD TO FIND THE VOLUME OF THE SOLID GENERATED BY REVOLVING THE REGION BOUNDED BY y  e x , y  0 , x  1, and x  2 ABOUT THE LINE x  3 .

17. A TANK IS FILLED WITH OIL (DENSITY CONSTANT = 94.5) TO A DEPTH OF 4 FEET. THE TANK IS SHAPED LIKE AN UPSIDE-DOWN CONE, 9 FEET TALL AND 6 FEET IN DIAMETER AT THE BASE. FIND THE WORK DONE IN EMPTYING THE OIL THROUGH A HOLE AT THE TOP OF THE TANK.

18. A FORCE OF 30 POUNDS IS REQUIRED TO STRETCH A SPRING 3 INCHES. FIND THE WORK DONE IN STRETCHING THE SPRING 8 INCHES.