Calculus I Exam 3 Review (2.7-3.7)
Review problems from pp. 200-201: work the following exercises from pp. 200-201: 1-4, 11-15, 17-25, 27, 30, 31, 33, 34, 36, 37, 39, 41, 52, 53, 67, 69-72 plus the following problems. In addition to the problems listed from the chapter review and these problems, all of your homework problems and quiz problems are fair game for the test as well. Please be sure to have your homework (2.7-3.7) completed and ready to hand in on Thursday.
1. Each side of a square is increasing at a rate of 3 cm/sec. At what rate is the area of the square increasing when the side length of the square is 5 cm?
2. Each side of a square is increasing at a rate of 2 cm/sec. At what rate is the area of the square increasing when the area of the square is 9 cm2?
3. The radius of a sphere is increasing at a rate of 2 mm/sec. How fast is the volume increasing when the diameter is 40 mm?
4. If a (spherical) snowball melts so that its volume decreases at a rate of 1.5 cm3/min, find the rate of change in the radius when the diameter is 8 cm.
5. Suppose y=2x+1, where x and y are functions of t.
a) If dxdt=3, find dydt when x = 4.
b) If dydt=2, find dxdt when x = 24.
6. Starting with the graph of y=ex, write equations for the graph that results from
a) shifting the graph 4 units to the left and 2 units down
b) vertically stretching the graph by a factor of 3 and reflecting over x-axis
7. Find an exponential function in the form fx=Cax for each of the graphs below.
a) b)
8. If fx=x3-3 , find f-15 and ff-1(-4).
Find f-1'a.
9. fx=x3-2 ; a=6 10. fx=x-5 ; a=1
Find f-1(x) and give its domain and range.
11. fx=1x+4 12. fx=x-2
Construct a right triangle to find each of the following. (No decimals!)
13. sintan-14 14. tansin-1x
Find the derivative of each function. Show work and simplify if possible.
15. fx=log45x3-x 16. fx=esinx2
17. y=lncos4x 18. y=x∙32x+1
19. fx=sin-1x2+5x 20. y=tan-1cos3x
21. Find exact values for each expression (no decimals).
a) sin-132 b) cos-1-22
c) sinh2 d) tanh0
e) sinh-10 f) cosh-11
Find the derivative of each function. Show work and simplify if possible.
22. fx=coshlnx 23. y=sech2et
Find the equation of the tangent line to each of the given curves at the given points.
24. y=ln 5x-4+7x; (1, 7) 25. y=ecosh3x; (0, e)
26. y=8log3x12; (9, 4) 27. y=cos-1(3-2x); (1, 0)