<p>I. FIND THE DERIVATIVE OF EACH FUNCTION. </p><p>2 ln(x) 1. f (x)  ln(tan(x)) 2. f (x)  x 3e x 3. f (x)  e x</p><p>4. f (x)  e 5x 5. f (x)  ln3 x 2 1 6. f (x)  x 4 ln(x)</p><p>II. FIND EACH INDEFINITE INTEGRAL. </p><p>1 3 x  4 7. dx 8. x 2e x 4 dx 9. dx  x  3   x 2  8x 1</p><p> sec 2 (x) e x e3x 10. dx 11. dx 12. dx  3x 1 tan(x)  x  3  e</p><p>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. </p><p>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.</p><p>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 .</p><p>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.</p><p>18. A FORCE OF 30 POUNDS IS REQUIRED TO STRETCH A SPRING 3 INCHES. FIND THE WORK DONE IN STRETCHING THE SPRING 8 INCHES.</p>