Mathematics 1600A/B- Midterm Exam Guide - Comprehensive Notes for the exam ( 124 pages long!)

0. (From the lecture notes) Give the range of (a) arcsin(r) (b) arccos(r) (c) arctan(x) 1, The Leaning Tower of Pisa is 179 feet high and at noon, its shadow measures 16.5 feet. Assuming the sun is directly overhead at noon, find the angle that the tower is inclined from the vertical.

Show all your work for full credit. The textbook, lecture notes, and elec- tronic devices with symbolic computing capacity are NOT allowed 1. Evaluate cos(x + 2y)dA, whe 2. Evaluate the following double integral Jo Jz 3. Evaluate the double integrals by converting them to polar coordinates. 2心ー昏 4. Evaluate the double integrals by converting them to polar coordinates. 5. Evaluate the triple integrals dxdydz, 2 drdzdy, 3. rdzdrd9. 6. Find the volume between the graph of the function f(r, y) - zy and the rect- angle R = {(z, y)1-2 3and-1 7. Evaluate the following double integrals y 5) 0 z+2 3. 2ded 8. Let S be the triangular region with vertices (0,0), (-1, 1), and (1, 1). (Sketch the region first!) . Find the centroid ofS . If the density at each point in S is proportional to the point's distance from the y-axis, find the mass of S.