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 on your scantron in EXACTLY this order. 00 Ms. Beck 004 Mr. Teng 005 Mr. Painter 006 Ms. Lubbe Fill in your scantron: NAME Last, first SUBJECT 46 - YOUR SECTION # TEST NO. A DATE PERIOD Fill out your scantron EXACTLY like this. Turn cell phones off and put them out of sight. Turn off all beepers and alarms. Do not write below this line. Part I total (48 points) (0 points) 4 (0 points) 5 (0 points) 6 ( points) 7 ( points) Part II total (5 points) Midterm Total (00 points) Your score 4 = Page of 8
Math 46 Midterm Version A Spring 0 Verify that your eam has 7 questions on 8 pages. If any pages are missing, please ask for another eam. The square brackets following an eam question number refer to a section/problem number in the tet. Problem numbers preceded by the symbol ~ are modeled on that problem from the tet, but not identical to it. Problem numbers without the symbol are identical to or very close to the problem from the tet. INSTRUCTIONS FOR PART I: Write your answers for these questions on a scantron (form 88-E or 88-ES) and mark only one answer per question. Scantrons will not be returned so mark your answers on your eam paper also; however, your grade in Part I will be determined solely by what you mark on your scantron. Each of the questions in this part counts 4 points, for a total possible score of 48 points. You may use an approved calculator. You may write on this eam or request scratch paper if needed.. [./Eample 4] sin 4 4 sin = and 9 9 sin 4 4 = because lim 0 9 9 sin lim = 0 sin 4 sin 4 4 (c) = = (d) 9 9 9 sin 4 sin cos sin (e) = and lim = 9 0 ( )( ) 9 sin 4 4 sin 4 sin 4 = and lim = 9 9 4 0 4 4 sin sin 4 4 sin = and lim = 9 9 0 4. [.4/~54] Which of the following defines g ( ) in a way that makes g ( ) continuous at =? = 6 9 g ( ) = 0 g ( ) = (c) g ( ) = (d) g ( ) = (e) ( ) 4 5 g = 6. [./0] Find the derivative of the function 7 6 7t ( ) (e) ( 6 7t ) 6 7t 4 t P( t) =. 6 7t (c) 7 (d) ( 6 7t ) Page of 8
Math 46 Midterm Version A Spring 0 4. [./47] Suppose f and g are both differentiable at = and that f () = 4, f () =, g() = and =, find ( ) g () =. If h( ) f ( ) g( ) h. 0 6 (c) 0 (d) (e) 4 5. [.5/7] Find f ( ) if cos sin cos + sin f ( ) =. cos cos sin cos ( ) (c) cos + sin ( cos ) cos + sin + (d) cos cos + sin (e) sin d 6. [.6/~4] Find ( e ) e d. e (c) e (d) e (e) e 7. [.7/47] Suppose that g is the inverse of a function f. If f () = 4 and f () =, find g (4). (c) 4 (d) 4 (e) not enough information given 8. [.7/~65] Find g ( ) if g( ) tan =. + (e) sec tan csc (c) + (d) ( + ) 9. [.8/7] Find an equation of the tangent line to the graph of y = ln at the point (,0 ). y = + y = (c) y = + (d) y = + (e) y = Page of 8
Math 46 Midterm Version A Spring 0 0. [.0/~6] Find the linearization ( ) (d) L( ) = L( ) = + ln (e) L of f ( ) ln ( cos e ) L( ) = + ln (c) L( ) = = + at = 0. L( ) = + ln. [./6] The total daily profit, in dollars, realized by the TKK Corporation in the manufacture and sale of dozen recordable DVDs is given by the total profit function P( ) = 0.00000 + 0.00 + 5 500 for 0 000. Find the level of production that will yield a maimum daily profit. 500 DVDs produced,667 DVDs produced (c) 5,000 DVDs produced (d) 5,000 DVDs produced (e) 0,000 DVDs produced. [./~4,8, ] Which of the following functions satisfy the hypotheses of the Mean Value Theorem? / I. f ( ),8 = on the interval [ ] 4/5 II. f ( ) = on the interval [ 0, ] III. f ( ) = ( ) on the interval [ 0, ] IV. sin if π < 0 f ( ) = 0 if = 0 III and IV only II and III only (c) I, II, III only (d) I, II, IV only (e) I, II, III and IV INSTRUCTIONS FOR PART II: For these questions, you must write down all steps in your solutions. Write legibly and carefully label any graphs or pictures. Draw a bo around your final answer. Partial credit will be given for those parts of your solution that are correct. The total value of the questions in this section is 5 points. Page 4 of 8
Math 46 Midterm Version A Spring 0. 0 pts [.4/~Eample 4] A child, lying on the ground, launches a rock from a slingshot vertically into the air. The height of the rock, in feet, t seconds after being launched is given by s( t) = 64t 6t, t 0. What is the initial velocity of the rock? How long will it take for the rock to reach its maimum height? (c) What is the maimum height attained by the rock? 4. 0 pts [.7/ ~Eample 5] Find dy d if + y = 6y. Find the -coordinates of all points on the curve where the tangent line is horizontal. Page 5 of 8
Math 46 Midterm Version A Spring 0 5. 0pts [.8/~6, ] Find the derivatives of the following functions. f ( ) = log + y = e Page 6 of 8
Math 46 Midterm Version A Spring 0 6. pts [.9/] Each side of a baseball diamond is 90 ft long. When a player who is between second and third base is 0 ft from second base, and heading toward third base at a speed of 8 ft/sec, how fast is the distance between the player and home plate changing? Round to two decimal places. Second base 90 ft Third base D First base Home plate Page 7 of 8
Math 46 Midterm Version A Spring 0 7. pts [.0/] Let y = +. Round each answer below to 4 decimal places. Find and y if changes from to.5. Find the differential dy; and use it to approimate y if changes from to.5. (c) Compute the error y dy in approimating y by dy. END OF EXAM IMPORTANT!! Is your scantron completed as instructed on the front page? Errors in completing scantrons will delay recording of test grades. Is your ID number on the test? Test papers without IDs cannot be accepted. Is there any work for grading on scratch paper? If so, make a note on the eam beside the problem and tell your instructor or proctor. Page 8 of 8