Math 2425 Final Exam Version A Spring 2016

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Math 5 Final Eam Version A Spring 6 Print your name legibly as it appears on your class roll. Last: First: ID Number: Check the appropriate section: 5 Mr. Glass (MoWe :PM-5:PM ) Dr.

1 Math 5 Final Eam Version A Spring 6 Print your name legibly as it appears on your class roll. Last: First: ID Number: Check the appropriate section: 5 Mr. Glass (MoWe :PM-5:PM ) Dr. Lacy (MoWeFr :AM-:5AM) Mr. Choi (MoWeFr :AM-:5AM) Dr. Epperson (TuTh :AM-:PM) Dr. Epperson (TuTh :AM-:PM) Fill in your scantron eactly as shown here: 5 Dr. Lacy (TuTh 9:AM-:5AM) Dr. Epperson (TuTh :AM-:PM) Dr. Adams (TuTh 6:PM-7:PM) An incorrect name or missing ID number will delay the return of your eam. 5 Dr. Ferguson (MoWe 5:PM-6:5PM) NAME Last Name, First Name SUBJECT 5-YOUR SECTION # TEST NO. FXA DATE PERIOD Bubble in A here. Write your ID number here. Truncate the leading. Bubble in. For eample, if your ID# is you input Turn cell phones off and put them out of sight. Turn off all beepers and alarms. Do not write below this line. Part I (5 points) ( points) Your score: 5 = ( points) ( points) ( points) 5 ( points) Part II Total (5 points) Final Eam Total: ( points) Your score: Page of 8

2 Math 5 Final Eam Version A Spring 6 INSTRUCTIONS FOR PART I: Write your answers for these questions on a scantron (form SC88-E) and mark only one answer per question. You may use an approved calculator. You may write on this eam or request scratch paper if needed. Scantrons will not be returned so mark your answers on your eam paper; however, your score in Part I will be determined solely by what you mark on your scantron. k k. Given that the Maclaurin series for sin is ( ) ( ) sin ( ) f =. +!, find the Maclaurin series for (a) k k ( ) + (b)! k k ( ) + (c)! k k ( ) +! (d) k k ( ) + (e)! k k+ ( ) ( )! 5. Let f( ) =. We use the second-degree Taylor polynomial of f at a = to approimate f (.9). Which of the following are TRUE? I. R (.9) c = for c (.9,) II. R (.9). III. R (.9).8 (a) I & III only (b) I & II only (c) I only (d) II only (e) III only. Compute the area of the region bounded by r = cosθ. (a) (b) π (c) (d) (e). Find the radius of convergence of the power series n. n=! ( n ) (a) (b) ½ (c) (d) (e) Page of 8

3 Math 5 Final Eam Version A Spring 6 5. Which of the following represents the volume of the solid generated by revolving the region bounded by y = and y = about the -ais. / / (a) π ( ) d (b) π ( y y ) dy c) π ( ) / (d) π ( ) d (e) None of these. y y dy 6. Find the arc length of the graph of y = on the interval,. (a) 7 5 (b) 7 (c) 6 (d) 7 (e) 7. Which one of the following represents the area of the surface generated when the curve revolved around the -ais? y = on [,] is 8 + dy (b) 9 y (a) / 8 / / (c) 9 y π y + dy π + 9 d (d) d (e) π + π + 9 d 8. Which of the following provide a parametric description of a line segment starting at point (,) and ending at point (,8)? (a) = 8t, y = ; t t (b) = t, y = 6 t; t (c) = t, y = t; t (d) = t, y = 8 t ; t (e) = t+, y = 8t+ 8; t 9. Which one of the following is an equation of the tangent to the curve corresponding to t =? = t, y = t + t at the point (a) y = + (b) y = (c) y = + (d) 8 y = (e) y =. Find a rectangular form for the polar equation r cosθ = sin θ. (a) (d) + y = (b) = sin θ, y = sin θ (c) + = (e) = y y + y = y Page of 8

4 Math 5 Final Eam Version A Spring 6 INSTRUCTIONS FOR PART II: For these questions, you must write down all steps, including the justification of any limits, to support your answer. Work shown is part of your grade. Write legibly and carefully. Draw a bo around your final answer. Partial credit will be awarded for those parts of your solution that are correct. π. ( points) On the graph provided below, shade the region R bounded by f( ) = sin +, =, =, and y =. Find the volume of the solid generated by revolving R about the y-ais. Page of 8

5 Math 5 Final Eam Version A Spring 6. ( points) n ( ) ( n + ) Determine if converges absolutely, converges conditionally, or diverges. Clearly identify n= n + any test(s) you are using and label all relevant data and/or properties and hypotheses needing verification. Page 5 of 8

6 Math 5 Final Eam Version A Spring 6. ( points) Compute the Taylor Series of the function f( ) = e centered at a = using the definition of Taylor series (that is, do not just compute it by manipulating a known Taylor series). Eplicitly show the first nonzero terms and show, in detail, how you computed them. Give an epression for the nth term of the series and show in detail how you computed it. Draw a bo around your final answer. Page 6 of 8

7 Math 5 Final Eam Version A Spring 6. ( points) (a) Draw the graphs of the polar equations r = + sinθ and r = sinθ together on the same polar grid provided below. (b) Find the points of intersection of the graphs. (c) Find the area of the polar region inside r = sinθ and outside r = + sinθ. Page 7 of 8

8 Math 5 Final Eam Version A Spring 6 5. ( points) A thin bar of length meters, represented by the interval, is made of an alloy whose density in units of kg/m is given by ρ( ) =. What is the mass (in kilograms) of the bar? 6 END OF EXAM IMPORTANT: Have you followed the directions on page? Failure to do so delays the return of eams. Page 8 of 8

Math 1426 Midterm 2 Version A Spring 2011

Math 1426 Midterm 2 Version A Spring 2011 Math 46 Midterm Version A Spring 0 Print your name legibly as it appears on the class rolls: Last First ID Number: 0 0 0 Check the appropriate section: 00 Dr. Krueger 00 Dr. Krueger (ESP) Write your name