MTH 132 Practice Exam 1Name:Section: Instructor:READ THE FOLLOWING INSTRUCTIONS.• Do not open your exam until told to do so.• No calculators, cell phones or any other electronic devices can be used on this exam.• Clear your desk of everything excepts pens, pencils and erasers.• If you need scratch paper, use the back of the previous page.• Without fully opening the exam, check that you have pages 1 through 9.• Fill in your name, etc. on this first page.• Show all your work. Write your answers clearly! Include enough steps for thegrader to be able to follow your work. Don’t skip limits or equal signs, etc. Includewords to clarify your reasoning.• Do first all of the problems you know how to do immediately. Do not spend toomuch time on any particular problem. Return to difficult problems later.• If you have any questions please raise your hand and a proctor will come to you.• There is no talking allowed during the exam.• You will be given exactly 90 minutes for this exam.• This is a practice exam. The actual exam may differ significantly from this practiceexam because there are many varieties of problems that can test each concept.I have read and understand the above instructions:. SIGNATUREPage 1 of 9MTH 132 Practice Exam 1Multiple Choice. Circle the best answer. No work needed. No partial credit available.1. (5 points) Find c such that the function f(x) =x2− 10, x ≤ c10x − 35, x > cis continuous everywhere.A. c = 10.B. c = 5.C. c =√10.D. c = 20.E. None of the above.2. (5 points) f(x) =x2− 9x2− 9x + 18is continuous on:A. (−∞, −3) ∪ (−3, 3) ∪ (3, 6) ∪ (6, ∞).B. (−∞, 6) ∪ (6, ∞).C. (−∞, 3) ∪ (3, ∞).D. (−∞, 3) ∪ (3, 6) ∪ (6, ∞).E. None of the above.3. (5 points) Consider proving that limx→3(2x − 5) = 1 using the formal definition of the limit. The largestvalue of δ > 0 so that the formal definition of the limit holds is:A. δ = 2.B. δ = 5.C. δ =2.D. δ =5.E. None of the above.Extra Work Space.Page 2 of 9MTH 132 Practice Exam 1Fill in the Blanks. No work needed. No partial credit available.4. Given the graph of f(x), label each statement either True or False:−4−3−2−11−2 −1 1 2 3 4 5 6y = f (x)(a) (3 points) : limx→3−f(x) = −1(b) (3 points) : limx→3+f(x) does not exist(c) (3 points) : f(x) is continuous at x = 4(d) (3 points) : f(x) is differentiable at x = 4(e) (3 points) : limx→4f(x) does not existExtra Work Space.Page 3 of 9MTH 132 Practice Exam 1Standard Response Questions. Show all work to receive credit. Please BOX your final answer.5. Find the following limits.(a) (8 points) limx→−2−x + 3x2+ 2x − 15(b) (8 points) limx→0sin(3x)5x(c) (8 points) limx→−3x2− 9x2+ 2x − 3Page 4 of 9MTH 132 Practice Exam 16. Given f(x) = cos(x) − sin(x)(a) (6 points) Find f0(x)(b) (6 points) Find the equation of the tangent line to f(x) at the point where x = π7. (14 points) Use the formal limit of the derivative to compute the derivative of f (x) = 5 +√x.Page 5 of 9MTH 132 Practice Exam 18. Differentiate the following functions. You need not simplify your answers.(a) (8 points) y = 3x4+ 2x sin(x)(b) (8 points) f(x) =√x1 + x2(c) (8 points) r =p2θ + sin(5θ)Page 6 of 9MTH 132 Practice Exam 19. (8 points) Show that the equation x5− x2+ 2x + 3 = 0 has at least one real root.Hint: Quote and use the IVT. You have to show why it applies.10. At time t, the velocity of an object is given by the function v = t2− 4t + 3.(a) (6 points) Find the object’s acceleration each time the velocity is zero.(b) (6 points) Find the object’s velocity each time the acceleration is zero.Page 7 of 9MTH 132 Practice Exam 111. (12 points) Given the function x2+ 2xy − y2+ x = 2, find an equation of the tangent line to the curveat the point (1, 2).12. (14 points) A kite is flying at an angle of elevation ofπ3radians. The kite string is being taken in at therate of 1 foot per second. If the angle of elevation does not change, how fast is the kite losing altitude?Page 8 of 9MTH 132 Practice Exam 1Please have your MSU student ID ready so that is can be checked.When you are completely happy with your work please bring your exam to the front to be handed in.Go back and check your solutions for accuracy and clarity. Make sure your final answers are BOXED .Congratulations you are now done with the exam!DO NOT WRITE BELOW THIS LINE.Page Points Score2 153 154 245 266 247 208 26Total: 150Page 9 of