MA 16500EXAM 3 INSTRUCTIONSVERSION 01November 13, 2017Your name Your TA’s nameStudent ID # Section # and recitation time1. You must use a #2 pencil on the scantron sheet (answer sheet).2. Check that the cover of your exam booklet is GREEN and that it has VERSION 01 onthe top. Write 01 in the TEST/QUIZ NUMBER boxes and blacken in the appropriatespaces below.3. On the scantron sheet, fill in your TA’s name (NOT the lecturer’s name) and thecourse number.4. Fill in your NAME and PURDUE ID NUMBER, and blacken in the appropriate spaces.5. Fill in the four-digit SECTION NUMBER.6. Sign the scantron sheet.7. Blacken your choice of the correct answer in the space provided for each of the questions1–12. All the answers must be marked on the scantron sheet. In case what ismarked on the scantron sheet is different from what is marked on the exam booklet, wecompute the final score based upon what is marked on the scantron sheet.8. While marking all your answers on the scantron sheet, you shouldshow your work on the exam booklet. In case of a suspicious activity of academicdishonesty and/or under certain circumstances, we require that the correct answer on thescantron sheet must be supported by the work on the exam booklet.9. There are 12 questions, each worth 8 points. The maximum possible score is8 × 12 + 4 (for taking the exam) = 100 points.10. NO calculators, electronic device, books, or papers are allowed. Use the back of the testpages for scrap paper.11. After you finish the exam, turn in BOTH the scantron sheet and the exam booklet.12. If you finish the exam before 8:55, you may leave the room after turning in the scantronsheets and the exam booklets. If you don’t finish before 8:55, you should REMAIN SEATEDuntil your TA comes and collects your scantron sheet and exam booklet.1Exam Policies1. Students must take pre-assigned seats and/or follow TAs’ seating instructions.2. Students may not open the exam until instructed to do so.3. No student may leave in the first 20 min or in the last 5 min of the exam.4. Students late for more than 20 min will not be allowed to take the exam; they willhave to contact their lecturer within one day for permission to take a make-up exam.5. After time is called, the students have to put down all writing instruments and remainin their seats, while the TAs will collect the scantron sheet and the exam booklet.6. Any violation of the above rules may result in score of zero.Rules Regarding Academic Dishonesty1. You are not allowed to seek or obtain any kind of help from anyone to answer questionson the exam. If you have questions, consult only your instructor.2. You are not allowed to look at the exam of another student. You may not compareanswers with anyone else or consult another student until after you have finished yourexam, handed it in to your instructor and left the room.3. You may not consult notes, books, calculators. You may not handle cell phones orcameras, or any electronic devices until after you have finished your exam, handed itin to your instructor and left the room.4. Anyone who violates these instructions will have committed an act of academic dis-honesty. Penalties for academic dishonesty can be very severe and may include an Fin the course. All cases of academic dishonesty will be reported immediately to theOffice of the Dean of Students.I have read and understand the exam policies and the rules regarding the academic dishonestystated above:STUDENT NAME:STUDENT SIGNATURE:2Questions1. Consider the function f(x) = xe−2x.Let M be the absolute maximum value of f(x) and m be the absoluteminimum value of f(x) on the closed interval [0, 2].What is M + m ?A.1e2B.12eC.e2+ 2e4D.e3+ 42e4E.1e32. The derivative of a function f is given byf0(x) = (x − 1)x(x + 1)2(x + 2)3.The function f has a local maximum only atA. x = −2B. x = 0C. x = −1 and x = 1D. x = −1 and x = 0E. x = −2 and x = 043. The second derivative of a function f is given byf00(x) = (x + 3)5(x + 1)4x3(x − 1)2(x − 3)How many inflection points does the graph of y = f(x) have?A. 0B. 1C. 2D. 3E. 454. Compute the following limits:(a) limx→0sin x − xx3; (b) limx→0sin xx + 1A. (a)13; (b) 1B. (a) ∞; (b) 0C. (a) ∞; (b) 1D. (a) −16; (b) 0E. (a) −16; (b) 165. Compute the following limitlimx→∞x + e3x1x.A. 1B. eC. e3D. 3E. ∞76. Find the equation of the slant asymptote to the graph of the functionf(x) =−6x4+ 2x3+ 32x3+ 1.A. y = 3xB. y = −3x − 1C. y = −3x + 1D. y = 6x − 2E. y = −6x + 287. Determine the exact value ofsin−113+ cos−113.HINT: Consider the functionF (x) = sin−1(x) + cos−1(x)over the interval [0,13].Compute its derivative and use Mean Value Theorem.A.π2B. πC. 0D.π4E. −π398. Computelimx→∞x tan5x.A. ∞B. 0C. 5D.15E. DNE109. Choose the picture from below that best describes the graph of the func-tionf(x) =x2x2− 4.A.B.C.D.E.1110. The sum of two positive number is 16.What is the smallest possible value of the sum of their squares?A. 162B. 128C. 98D. 72E. 501211. A box with square base and open top must have a volume of 4 m3.Find the height of the box that has the smallest possible surface area.A. 4B. 3/2C. 1/2D. 1/4E. 11312. Find the equation of the line through the point (4, 3) that cuts off thetriangle of least area from the first quadrant.A. y = −43x + 8B. y = −43x +253C. y = −x + 7D. y = −34x + 6E. y