MAT 265 – Calculus for Engineers-I Student Name : Instructor : Instructor Student ID : Exam # 2 (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 cheatingMAT 265 – Calculus for Engineers-I EXAM # 2 Instructor School of Mathematical & Statistical Sciences – Arizona State University PART I – Multiple choice. Please circle your answer choice on the exam and fill in the answer grid on the last page. Use the space beside the answers to work your solution. Use the following table to answer questions 1 – 3.  () () () () 0 3 -1 2 -4 1 3 2 4 6 2 1 8 5 7 3 2 2 7 9 1. If )(4sin2)(3)( xfxxgxxh+−=, what is )0('h? a. 5 b.3 c. −6 d.12 e. None of the above 2. If )(cos3)(xgxxxh+= , what is )0('h? a. 1 b.−0.75 c. −6 d.12 e. None of the above 3. If ))3(()(2xfgxh = , what is )1('−h? a. 8 b.7 c. −49 d.−294 e. None of the above 4. The radius of a circular disk is given as 5 cm with a maximum error in measurement of 0.01 cm. Use differentials to estimate the maximum error in the calculated area of the disk. a. π10 b.10π c. 000,10π d.π25 e. None of the above 5. Use ( + )≈ ()+  to approximate .05.83 a. 2.004158125 b. 2.004158016 c. 2.004163333 d. 2.004166667 e. None of the aboveMAT 265 – Calculus for Engineers-I EXAM # 2 Instructor School of Mathematical & Statistical Sciences – Arizona State University 6. Find the exact limit: xxx)5(75)5(74lim−−∞→ a. 77 b. 54 c. √7d. ∞ e. None of the above 7. Find the exact limit: )]3ln([lim2+−∞→xxxe a. 89 b. 910 c. 1 d. ∞ e. None of the above 8. If = 4, evaluate )4,2(dxdy. Hint: take the natural logarithm of both sides. a. ()() b. 1 c. ()() d. 4ln(4) e. None of the above 9. Suppose14)( += ttf. Evaluate)2(''f. a. 274− b.274 c. 32− d.32 e. None of the aboveMAT 265 – Calculus for Engineers-I EXAM # 2 Instructor School of Mathematical & Statistical Sciences – Arizona State University 10. Suppose 1,112)( >−+= xxxxf. Find a formula for )(1xf−, the inverse function. a. 2,12>+−xxx b.2,21>−+xxx c. 2,21>−+xxx d.2,12>+−xxx e. None of the above 11. Suppose 1,112)( >−+= xxxxf,use 111( ) ( )( ( ))f af f a−−′=′ to find )3()(1′−f. a. 72 b.72− c. −3 d.3 e. None of the above 12. Find )1('fif )ln()(2 xexxf= . a. 0 b.1 c. e d.3 e. None of the above 13. Use L’Hospital’s Rule to evaluate xxxx38)10sin(lim0+→. a. 6 b.3 c. 1 d.Does not exist e. None of the above 14. Use L’Hospital’s Rule to help evaluate xxxln7)2ln(lnlim+∞→. a. 2 b.ln 2 c. 2e d.Does not exist e. None of the aboveMAT 265 – Calculus for Engineers-I EXAM # 2 Instructor School of Mathematical & Statistical Sciences – Arizona State University PART II – Free response. Show all your work 1. A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight east. When the cruiser is 0.6 mi north of the intersection and the car is 0.8 mi to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph. If the police cruiser is moving at 60 mph at the instant of measurement, what is the speed of the car? [10 pt] + = (2point) 2"+ 2"= 2"(2points) When  = 0.8and = 0.6, =√0.64 + 0.36 = 1, so (1point) (0.8),--./ +(0.6)(−60)=(1)(20)(3points) So"=560.8= 7034ℎ(2points) 2. Find an equation of the tangent line to the curve 23 5 cos( ) 7 5 at (1,0)x xy y x+ − = − . [10 pt] (3+ 5 − cos())=(7 − 5)(1point) 6 + 5 + 5+ sin()= 7(3points) =7 − 6 − 55 + sin()(2points)