Math 116 — First MidtermOctober 14, 2015UMID:Initials:Instructor:Section:1.Do not open this exam until you are told to do so.2.Do not write your name anywhere on this exam.3.This exam has 11 pages including this cover. There are 10 problems. Note that the problemsare not of equal difficulty, so you may want to skip over and return to a problem on whichyou are stuck.4.Do not separate the pages of this exam. If they do become separated, write your UMID onevery page and point this out to your instructor when you hand in the exam.5.Please read the instructions for each individual problem carefully. One of the skills beingtested on this exam is your ability to interpret mathematical questions, so instructors willnot answer questions about exam problems during the exam.6.Show an appropriate amount of work (including appropriate explanation) for each problemso that graders can see not only your answer, but also how you obtained it. Include units inyour answer where that is appropriate.7.You may use a TI-84, TI-89, TI-Nspire or other approved calculator.However, you mustshow work for any calculation which we have learned how to do in this course. You are alsoallowed two sides of a 300×500note card.8.If you use graphs or tables to find an answer, be sure to include an explanation and sketchof the graph, and to write out the entries of the table that you use.9.Turn off all cell phones, pagers, and smartwatches, and remove all headphones.ProblemPointsScore11627394105116779813910108Total100

Math 116 / Exam 1 (October 14, 2015)DO NOT WRITE YOUR NAME ON THIS PAGEpage 21. [16 points]Supposeg(x) is a function with the following properties:•Z15g(x)dx= 7.•Z53g(x)dx=-3.•g(x) is odd.In addition, a table of values forg(x) is given below.x012345g(x)02-1-3-11Calculate (a)-(c)exactly. Show your work and do not write any decimal approximations.a. [4 points]Z√31xg(x2)dx.b. [4 points]Z51xg0(x)dx.c. [3 points]The average value ofg(x) on [-5,-1].d. [5 points]ApproximateZ4xg(x)dxusing TRAP(2). Write out all the terms of your sum and your final answer.2

Math 116 / Exam 1 (October 14, 2015)DO NOT WRITE YOUR NAME ON THIS PAGEpage 3