NAME SCOREJoel RobbinCalc 221 Final Exam, Monday December 15, 1997Circle your section.311 Hollingsworth 8:00 TR B305 Van Vleck312 Hollingsworth 9:30 TR B305 Van Vleck313 Nilsen 9:30 TR B203 Van Vleck314 Kent 11:00 TR B305 Van Vleck315 Resnick 11:00 TR B309 Van Vleck316 Kent 1:00 TR B305 Van Vleck317 Resnick 2:30 TR B305 Van Vleck318 Nilsen 2:30 TR 3335 SterlingI 20 PointsII 20 PointsIII 20 PointsIV 20 PointsV 20 PointsVI 20 PointsVII 20 PointsVIII 20 PointsIX 20 PointsX 20 PointsTotal 200 PointsExtra Credit 25 PointsShow your reasoning.NAME SCORECalc 221 Final Exam, Monday December 15, 1997Circle your section.331 Herzig 7:45 TR B211 Van Vleck333 Huedepohl 9:55 TR B329 Van Vleck334 Huedepohl 11:00 TR B337 Van Vleck335 Kung 12:05 TR B333 Van Vleck336 Kung 1:20 TR B325 Van Vleck337 Herzig 2:25 TR B321 Van VleckI 20 PointsII 20 PointsIII 20 PointsIV 20 PointsV 20 PointsVI 20 PointsVII 20 PointsVIII 20 PointsIX 20 PointsX 20 PointsTotal 200 PointsExtra Credit 25 PointsShow your reasoning.NAME SCORECalc 221 Final Exam, Monday December 15, 1997Circle your section.001 CAUGHMAN, JOHN 8:50 B223 Van Vleck002 MILLER 9:55 B223 Van Vleck003 KERSEY, SCOTT 11:00 B223 Van Vleck007 LANG, MICHAEL 12:05 B223 Van Vleck010 APPS, PHILIP 1:20 B223 Van Vleck011 PONOMARENKO, VADIM 2:25 B223 Van Vleck015 HILDEBRAND, JEFF 3:30 B223 Van VleckI 20 PointsII 20 PointsIII 20 PointsIV 20 PointsV 20 PointsVI 20 PointsVII 20 PointsVIII 20 PointsIX 20 PointsX 20 PointsTotal 200 PointsExtra Credit 25 PointsShow your reasoning.I. (20 points.) (a) Finddydxwhen y = ln(2 + ex).(b) Findd2ydx2for y as in (a).II. (20 points.) (a) EvaluateZ32x2dxx3− 1.(b) Evaluate limx→3 1x − 3Zx3sin(t)tdt!.III. (20 points.) A population of bacteria triples in three hours. Assuming exponential growth,how long does it take to double?IV. (20 points.) Find the points on the hyperbola y2− x2= 4 which are closest to the point(2, 0).V. (20 points.) (a) Find the equation for the tangent line to the curve y2= x3+ 3 at the point(x, y) = (1, 2).(b) Is this tangent line above the curve? Why or why not?VI. (20 points.) (a) Evaluate limn→∞nXi=1"31 +2in5− 6#2n.(b) Evaluate limx→∞tan−1(x).VII. (20 points.) The velocity function for a particle moving along a line isv(t) = 3t − 12, 0 ≤ t ≤ 5.(a) Find the displacement (net change in position) from t = 0 to t = 5.(b) Find the total distance travelled from t = 0 to t = 5. (Note that the velocity changes sign.)VIII. (20 points.) Find the interval on which the curve y =Zx0dt1 + t + t2is concave up.IX. (20 points.) Find the volume generated by revolving the region bounded by the lines x = a,x = b , y = 0 and the curve y =√1 − x2about the x-axis. (Assume that a and b are constantsand 0 < a < b < 1.)6-x = 1x = ax = bX. (20 points.) State and prove the formula for the derivative of the inverse sine functionsin−1(x). You may assume without proof that the derivative of the sine function is the cosinefunction.EXTRA CREDIT. (25 points.) A high speed train accelerates at (1/2) meter/sec2untilit reaches its maximum cruising speed of 30 meters per second; after it reaches this maximumcruising speed it remains at that speed. If it starts from rest, how far will it go in 10 minutes?AnswersIa.ex2+exIb.2ex(2+ex)2IIa.13(ln(26) − ln(7))IIb.sin(3)3III.3 ln(2)ln(3)IV. (1,√5) and (1, −√5)Va. (y − 2) =34(x − 1)Vb. Tangent line is below curve (at least locally) because concavity is upward.VIa.1236− 12 −12VIb.π2VIIa. −452VIIb.512VIII. (−∞, −12)IX. π[(b −13b3) − (a −13a3)]EXTRA CREDIT 17100
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