## mat265_ex1

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## mat265_ex1

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- Pages:
- 5
- School:
- Arizona State University
- Course:
- Mat 265 - Calculus for Engineers I

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MAT 265 Calculus for Engineers I Student Name Instructor XXXXXXXX Student ID Exam 1 Form A Class Time Honor Statement By signing below I confirm that I have neither given nor received any unauthorized assistance on this exam This includes any use of a graphing calculator beyond those uses specifically authorized by the School of Mathematical and Statistical Sciences and my instructor Furthermore I agree not to discuss this exam with anyone until the exam testing period is over In addition my calculator s memory and menus may be checked at any time and cleared by any testing center proctor or School of Mathematical and Statistical Sciences instructor Signature Date Instructions 1 The exam consists of two parts multiple choice worth 70 and free response show your work worth 30 Please read each problem carefully 2 There are 14 multiple choice questions worth 5 points each Please circle your answer choice on the exam AND fill in the answer grid on the last page 3 Provide complete and well organized answers in the free response section 4 Answers in the free response section without supporting work will be given zero credit Partial credit is granted only if work is shown 5 No calculators with Qwerty keyboards or ones like the Casio FX 2 TI 89 TI 92 or TI nspire that do symbolic algebra may be used 6 Proctors reserve the right to check calculators 7 Please request scratch paper from the testing center staff if you need 8 The use of cell phones is prohibited TURN YOUR CELL PHONE OFF Do not allow your cell phone to ring while you are taking the exam Do not use the calculator on your cell phone If a proctor sees you using a cell phone they will take your exam and you will be reported to the Dean of Students for cheating MAT 265 Calculus for Engineers I EXAM 1 Instructor PART I Multiple choice Choose the response that best completes the statements or answers the question Please circle your answer choice on the exam and fill in the answer grid on the last page Show your work on the space provided 1 Find the domain of the function f x A 3 3 25 x 2 x 3 B 5 3 3 5 C 5 3 3 5 E None of the others D 5 5 2 Check whether the following function is even odd or neither 5 3 A f x is even B f x is odd C f x is neither D f x is both E None of the others 3 Given the functions 7 and 4 5 find and simplify f o g x A 12 35 25 D 12 5 25 x 2 2 x 11 Use the function g x 10 cos x 3 x 6 B 12 35 25 C 12 5 25 E None of the others if x 1 if 1 x 2 to find the limits in questions 4 and 5 if x 2 4 Consider lim g x which of the following is true DNE means does not exist x 1 A lim g x 10 lim g x 10 lim g x 0 B lim g x 10 lim g x 10 lim g x 10 C lim g x 10 lim g x 10 lim g x 1 D lim g x 10 lim g x 10 lim g x DNE x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 E None of the others 5 Consider lim g x which of the following is true DNE means does not exit x 2 A lim g x 10 lim g x 0 lim g x 0 x 2 B lim g x 10 lim g x 0 lim g x 10 x 2 x 2 x 2 C lim g x 10 lim g x 0 lim g x DNE x 2 x 2 x 2 x 2 x 2 D lim g x 0 lim g x 0 lim g x 0 x 2 x 2 x 2 E None of the others 3x 2 2 x 8 x 2 x 2 6 Algebraically calculate the following limit lim A 0 B 10 C does not exist 7 Algebraically calculate the following limit lim x 4 A 1 3 B 0 C D 2x 1 3 x 4 D does not exist School of Mathematical Statistical Sciences Arizona State University E None of the others E None of the others 2 MAT 265 Calculus for Engineers I EXAM 1 Instructor 3 x if x 1 f x 4 5 x if x 1 2 8 Explain why the following function is discontinuous at x 1 A f is not defined at x 1 B The graph of f has a hole at x 1 C lim f x DNE x 1 B D f is a picewise fuction E None of the others 9 Explain why the following function is discontinuous at x 3 A f is not defined at x 3 D lim f x f 3 x 3 B lim f x DNE 5 2 x if x 3 f x x 5 if x 3 C f has jump discontinuity x 3 x 3 E None of the others cx 6 if x 2 10 For what value of the constant c is the function f x continuous on 3 x 2c if x 2 A c 3 B c 3 C c 2 D c 2 E None of the others D E None of the others 3 5 E None of the others 4x 2 5 x 7 8 x 2 11 Calculate the following limit lim A 1 2 B C does not exist 9x 4 1 x 5 x 2 3 x 1 12 Calculate the following limit lim A does not exist 13 B 5 C 9 5 D Use your calculator to graph f x 3 x 4 then explain why f is not differentiable at x 4 A At x 4 the tangent line to the graph of f is vertical B At x 4 the tangent line to the graph of f is horizontal C The function is not defined at x 4 D The function is not continuous at x 4 E None of the others 14 Let 5 3 2 sin 7 0 2 0 A 0 B 3 C 1 School of Mathematical Statistical Sciences Arizona State University D 5 E None of the others 3 MAT 265 Calculus for Engineers I EXAM 1 Instructor PART II Free response Show all your work 1 Algebraically find an equation of the tangent line to the curve f x x at the point with abscissa x 4 Since So 2 4 or 2 Let f x 4 we have and therefore the slope of the tangent line is 6 points 1 4 points 6 Use the limit definition of the derivative to find f x 2x 3 De0inition So 10 pt lim 5 7 6 6 2 3 2 …

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