ex1solutionsfall05 - Math 116 First Midterm Exam SOLUTIONS...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 116 – First Midterm Exam SOLUTIONS Name: Instructor: Section Number: 1. Do not open this exam until you are told to begin. 2. This exam has 11 pages including this cover. There are 9 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator. You are also allowed two sides of a 3 by 5 notecard. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to show how you obtained your answer. 8. Please turn of all cell phones and pagers and remove all headphones. Problem Points Score 1 8 2 13 3 11 4 12 5 11 6 13 7 12 8 10 9 10 Total 100
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 1. (8 points) Consider the functions f and g deFned below. Assume a is a nonzero constant. f ( x ) = ( x a ) 2 x , g ( x ) = x cos( ax ) , (a) (4 pts.) ±ind the family of antiderivatives of f ( x ). Show step-by-step work. We have f ( x ) = x 2 2 ax + a 2 x = x 3 / 2 2 ax 1 / 2 + a 2 x 1 / 2 . So, i f ( x ) dx = 2 5 x 5 / 2 4 3 ax 3 / 2 + 2 a 2 x 1 / 2 + C. (b) (4 pts.) ±ind the family of antiderivatives of g ( x ). Show step-by-step work. Using integration by parts, u = x u = 1 v = cos( ax ) v = sin( ax ) a . Then, i x cos( ax ) dx = x a sin( ax ) i sin( ax ) a dx = x a sin( ax ) + cos( ax ) a 2 + C.
Background image of page 2
3 2. (13 points) In the magical tale of Harry Potter and the Half-blood Prince, Harry and professor Dumbledore go in search of a horcrux, a dark magic device created by the dark wizard Voldemort in order to hide and preserve a piece of his soul. To get to the horcrux, Dumbledore must drink a lethal green elixir Flled with dark power. Harry’s task is to scoop some of the magic liquid into a goblet, feed it to Dumbledore, then turn around and scoop some more liquid into the goblet, repeating these steps until the elixir is gone. Harry notices that, after the Frst glass, Dumbledore’s drinking speed increases at a decreasing rate. By the end, Dumbledore is drinking as slowly as possible. The graph below represents Dubledore’s drinking speed, s (in ±uid ounces per second) against time, t (in seconds.) s t 1 2 3 4 4 5 6 8 12 16 20 24 28 32 (a) (5 pts.) Sketch the amount a of the elixir that Dumbledore has drunk as a function of time t during the Frst 32 seconds after he started drinking. Include scales on each axis, and label them appropriately. Clearly indicate on your sketch the heights of the graph of
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

ex1solutionsfall05 - Math 116 First Midterm Exam SOLUTIONS...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online