MTH 132 Practice Exam 2Name: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 8.• 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 8MTH 132 Practice Exam 2Multiple Choice. Circle the best answer. No work needed. No partial credit available.1. Write the following sums in Σ-notation.(a) (5 points) 6 + 12 + 24 + 48 + 96 + 192 =A.6Xi=16 · 2i−1B.6Xi=12 · 6iC.10Xi=13 · 2iD.6Xi=1i3E. None of the above.(b) (5 points) 7 − 11 + 15 − 19 + 23 − 27 + 31 − 35 + 39 =A.8Xi=0(−1)i(7i + 4)B.8Xi=0(7i + 4)C.8Xi=0(−1)i(4i + 7)D.8Xi=0(4i + 7)E. None of the above.Extra Work Space.Page 2 of 8MTH 132 Practice Exam 2Fill in the Blanks. No work needed. No partial credit available.2. Consider the function f(x) =3√x(a) (5 points) The linearization of f at x = 1 is L(x) = .(b) (5 points) Use your answer to (a) to estimate3√1.1 ≈ .3. Given thatZ3−2f(x)dx = 4,Z31f(x)dx = 5, andZ31g(x)dx = −2, find(a) (5 points)Z−21f(x)dx =(b) (5 points)Z312 · g(x) − f(x)dx =(c) (5 points)Z3−25 dx =Extra Work Space.Page 3 of 8MTH 132 Practice Exam 2Standard Response Questions. Show all work to receive credit. Please BOX your final answer.4. Consider the curve y = f (x) =x2− 3x − 2.(a) (6 points) Find the intervals on which f (x) is increasing and the intervals on which f (x) is de-creasing.(b) (4 points) Find any local extreme values and identify whether each is a local minimum or localmaximum.(c) (6 points) Find the intervals on which f(x) is concave up and the intervals on which f (x) is concavedown.(d) (4 points) Find any points of inflection.(e) (5 points) Give equations for all asymptotes.(f) (4 points) Find the y-intercept and all x-intercepts.(g) (6 points) Use the above parts to sketch the graph of y.Page 4 of 8MTH 132 Practice Exam 25. (10 points) Use Newton’s method to approximate the positive root of the function x2−3. Starting withan initial guess of x1= 2, find x2.6. Find the anti-derivatives of the following functions.(a) (6 points) f(x) =3x3+ 5x(b) (6 points) g(x) = cos2(3y)(Hint: use the double-angle formula for cosine: cos(2θ) = 1 − cos2(θ))(c) (6 points) h(x) =3t3+ t22√tPage 5 of 8MTH 132 Practice Exam 27. (12 points) Given the acceleration of an object, a(t) = −2t + 2, the velocity at t = 1 second, v(1) = 4and the position at t = 0 s(0) = 3. Find the object’s position, s(t), as a function of time.8. Let f(x) =√x + 1.(a) (10 points) Use the Mean Value Theorem to show that there exists a point c in (1, 4) such thatf0(c) =13. (You must verify the hypotheses AND conclusion of the Mean Value Theorem).(b) (5 points) Find this point c.Page 6 of 8MTH 132 Practice Exam 2(c) (5 points) Could the Mean value theorem be applied to the function f (x) = |x −2| on the interval(1, 4)? Explain.9. (20 points) Suppose you want to build a fish tank in the shape of a rightrectangular box with square base and no top which will hold 6 cubic feet of water.The glass for the sides costs $ 1 per square foot, and the metal for the bottom costs$ 1.50 per square foot. What dimensions for the tank will minimize the cost?sshPage 7 of 8MTH 132 Practice Exam 2Please 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 103 254 355 286 277 25Total: 150Page 8 of