[MA129] - Final Exam Guide - Everything you need to know! (80 pages long)

560 Test exercise 7 Write out the solutions carefully. They all quite straightforward. 1 Differentiate the following with respect to x: 38 (b) (Sr +3,- (O cosh, (a) tan 2x sin, 4x er)-3x 2 lfx2 + ,2-2x+2y-23,find/rand얽at the point where x--zy. 4 Ifx-11-cos" and y-3(.-sin") find a and a: in their simple (d) kg.dr.3x-1) sina 田 (x+1 diy when r,y,4ay2以 3 Find an expression for forms Further problems 7 39 1 Differentiate with respect to (b) In(secx+tanx (c) sinxcos'x 2 Find when: a)y-14 cosx if y is a function of x, and x-T+1 show that훑-x(1-x)dr 3 5 Differentiate coshx-1 coshx1 ",.tow. "r-wrmF} o, ,.刍 7 If(x-n'-A(x + y. prove that (2x + y -x+2y. If.e + 2xy + 3,-이.prove that (x + 3 '헒+2tx2 + 2xy + 9 Scanned by CamScanner

7, y=(x-29, y=x 8. y = sin x, y = 2x/T, x > 0 10, 4x + y2= 12, x = y 11-20 Sketch the region enclosed by the given curves and find its area. 11, y = 12-r', y = x2-6 12. y=x2, y=4x-x2 14. y = cos x, y = 2-cos x, 15. x = 2y, x=4+y,2 16.x=y", y 0 2π 18. y = 1x1, y = x2-2 Unless otherwise noted, all content on this page is © Cengage Learning Graphing calculator or computer required CAS Computer algeb Copyright 2012 Cengage Leaming. All Rights Reservod May not be copied, scanned, or duplic Editorial revicew has deemed that any suppressed content does not materially affect the overal

8. Determine whether the vectors a = 121 - 20j + 16k and b = - 9i + 15j - 12k are parallel, perpendicular, or neither. 9. Find (to the nearest degree) the three angles of the triangle with vertices at A(1, 1, 1), B(3, -2, 3), and C(3, 4, 6). 10. Find the vector proj a b if a = 21 + 10j-11k and b = 21 + 2j + k. DIRECTIONS: The purpose of this assignment is to evaluate your knowledge of the topics covered in chapter 12 of the text. Read all directions carefully. Make sure to answer all parts of the question. Show all necessary work to receive full credit. Do all work by hand. Circle and label all answers. Please write neatly. Once you have completed the homework assignment, then please scan in your assignment and save it as a PDF file. Also, please make sure that the scan is readable (i.e. the text is dark enough to read). If the assignment is illegible (i.e. extremely messy handwriting or too light of copy) and I cannot read it, then I will not grade it. After have scanned the assignment in and saved it as a PDF file, then submit the assignment in the chapter 12 assignment dropbox. This assignment is worth 200 points. Good luck.