Tracie Catania
Spring 2002Name
The Math 20B Final Exam
Please show all work on separate paper. Label problem numbers CLEARLY and box your answers! Good Luck!
Find the derivative of each of the following functions:
1.2.
Evaluate the integrals (show all work):
3.4. 5.
6.a. Find the limit: b. Find the limit of the sequence:
7.Determine whether each series converges (conditionally or absolutely) or diverges. If the series is GEOMETRIC in form, give the sum of the series. Give reasons for your answers!!!
a. b.
8. Given the power series , find the interval and radius of convergence.
9.Use a known Maclaurin series to find a series for . Then use the series to find a series for.
10.The centroid of the region bounded by and is . Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region around y=2.
11.SET UP an integral to find the surface area obtained by revolving on around the x-axis.
12.The ends of a trough are equilateral triangles with sides 8 m long with vertex at the bottom. It contains water (density ) and the water level is 1 m from the top of the trough. SET UP an integral to find the hydrostatic force on one end of the trough.
13.Given the polar function:
a. Sketch a graph.
b. SET UP an integral that would find the area enclosed by of one loop of .
c. SET UP an integral that would find the arclength ofthe curve.
14.Given the curve:
a. Sketch a graph. Find and label values of corresponding to points at the pole.
b. FIND for .
c. SET UP integrals to find the area between the outer and inner loops.
d. SET UPan integral to find the length of the outer loop.
Grades will be posted on the door to this building by 10:30 Tuesday. Finals will not be returned, but I will keep them in my office for one year – stop by if you’d like to review your exam. Good luck next semester and …
Happy Summer Vacation!