13 Questions on Calculus II - Exam 1 | MATH 112, Exams of Calculus

Download 13 Questions on Calculus II - Exam 1 | MATH 112 and more Exams Calculus in PDF only on Docsity! Test 1 Math 112 February 8, 2005 NAME 9:20, 10:20, 12:20 Circle your class time. • No calculator is allowed. Do not round off answers. If you get 10/6 as an answer, you should leave your answer as 5/3. No decimal approximations, please. • If you have any questions, please raise your hand and ask. The worst that will happen is that I will say, “I can’t tell you.” • Do the problems that you find easiest first. Take deep breaths between questions. • There are 100 points on this exam, and you have 110 minutes. • I hope you all do well. Good luck! Question Points Points Earned 1a 10 1b 8 2 9 3 9 4 9 5 7 6 7 7 7 8 7 9 7 10 5 11 5 12 5 13 5 TOTAL 100 Take three deep breaths. What information have you been given? What information do you need? How can you get from one to the other? 1. (30 pts.) Set up but DO NOT EVALUATE an integral that equals the volume of the solid described below. (a) The volume is generated by revolving the region bounded by x = y2 − 16 and y = x + 4 about the line x = 1. (b) The volume is generated by revolving the region bounded by x = y2 − 16 and y = x + 4 about the line y = 5. (The region is the same as in Part a.) 7. ∫ x2 sec(x3 + 2) tan(x3 + 2) dx 8. Stop simplifying when your answer is entirely made up of numbers. ∫ 0 −2 3t5 √ 1 − t3 dt 9. ∫ ex √ 1 − e2x dx 10. (5 pts.) Evaluate tan−1(1): 11. (5 pts.) Evaluate sin−1 ( sin ( 4π 3 )) : 12. (5 pts.) Find and simplify dy dx for y = arctan(ex) − cos ( sin−1(x) ) . 13. (5 pts.) Simplify the following to an expression without trig or inverse trig functions. tan ( cos−1 ( x 5 ))