Exam1_115_Solutions calc1 - M ATH 115 F IRST M IDTERM...

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

View Full Document Right Arrow Icon
M ATH 115 –F IRST M IDTERM February 5, 2008 N AME : ****SOLUTIONS**** I NSTRUCTOR : S ECTION N UMBER : 1. Do not open this exam until you are told to begin. 2. This exam has 9 pages including this cover. There are ?? 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 arrived at your solution. 8. Please turn off all cell phones and pagers and remove all headphones. P ROBLEM P OINTS S CORE 1 10 2 12 3 14 4 6 5 8 6 14 7 12 8 12 9 12 T OTAL 100
Image of page 1

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

View Full Document Right Arrow Icon
2 1. (2 points each) For each of the following, circle all statements which MUST be true. (a) Let f be a non-decreasing differentiable function defined for all x . f ( x ) 0 for all x . f ′′ ( x ) 0 for all x . f ( x ) = 0 for some x . (b) Let f and g be continuous at x = - 1 , with f ( - 1) = 0 and g ( - 1) = 3 . f · g is continuous at x = - 1 . g f is continuous at x = - 1 . f g is continuous at x = - 1 . (c) Let f be differentiable at x = 2 , with f (2) = 17 . lim x 2 f ( x ) = 17 . lim h 0 f (2 + h ) - f (2) h = 17 . lim h 0 f (2 + h ) - f (2) h exists. (d) Let f be defined on [ a, b ] and differentiable on ( a, b ) , with f ( x ) < 0 for all x in ( a, b ) . If a < c < d < b , then f ( c ) > f ( d ) . f ′′ ( x ) > 0 for some x in ( a, b ) . f is continuous on ( a, b ) . (e) Let f be a twice-differentiable function that is concave-up on ( a, b ) , with f ( a ) = 4 and f ( b ) = 1 . For some x in ( a, b ) , f ( x ) = 2 . 5 . For all x in ( a, b ) , f ′′ ( x ) 0 . f ( a ) f ( b ) .
Image of page 2
3 2. If you pluck a guitar string, a point P on the string vibrates. The motion of the point P is given by g ( t ) = A cos(220 π t ) , where g ( t ) is the displacement (in mm) of P from its position before the string was plucked, t is the number of seconds after the string was plucked, and A is a positive constant. (a) (6 points) Sketch a graph of g ( t ) , for 0 t 1 / 55 , on the axes below. Be sure to indicate A on your sketch. t g ( t ) 1 55 12 880 9 880 6 880 A (b) (3 points) Sketch tangent lines to your graph at t = 6 / 880 , t = 9 / 880 , and t = 12 / 880 . Use these to write the numbers g (6 / 880) , g (9 / 880) , and g (12 / 880) in order from least to great- est.
Image of page 3

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

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

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern