Work the following on notebook paper. No calculator. Find the derivative. Do not leave negative exponents or complex fractions in your answers.
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1 ALULUS B WORKSHEET ON 8. & REVIEW Find the derivative. Do not leave negative eponents or comple fractions in your answers. sec. f 8 7. f e. y ln tan. y cos tan. f 7. f cos. y 7 8. y log 7 Evaluate the given integrals sec tan 7sec d. d. 8 d 7. cos e e d d 8.. cos 7 d d 9.. sin cos d. d. 9 d sin d. 7 d 9.. e ln d. e d
2 Answers to Worksheet on 8. & Review. 8 sin cos.. sec tan. 7. sec tan. e sec tan cos ln sin ln 9. 7 sec 9 sec 7tan. 8. sin sin ln 7. sin sin e 8. 7 ln7 9. arcsin. arctan. ln arctan. arcsin
3 ALULUS B WORKSHEET ON INTEGRATION BY PARTS AND REVIEW Work these on notebook paper. No calculator ecept on problem. Evaluate.. 7. e sin d e d. sec d 8. e d.. sin d 9. ln d ln d. arcsin d e e. d e. arctan d. e d. ln for 8. Let f Find f d. for.. Find dy d in terms of and y, given y d cos sin. Use your calculator on problem.. A tank contains gallons of oil at time t = hours. Oil is being pumped into the tank at a rate is measured in gallons per hour and t is measured in hours. Selected, where Rt values of Rt Rt are given in the table below. Rt t (hours) 9 (gallons per hour) (a) Estimate the number of gallons of oil in the tank at t = hours by using a trapezoidal approimation with four subintervals and values from the table. Show the computations that lead to your answer. (b) Estimate the number of gallons of oil in the tank at t = hours by using a right Riemann sum with four subintervals and values from the table. Show the computations that lead to your answer. (c) A model for the rate at which oil is being pumped into the tank is given by the function Gt, where Gt is is measured in gallons per hour and t is measured in ln t hours. Use the model to find the number of gallons of oil in the tank at t = hours.
4 Answers to Worksheet on Integration by Parts and Review. e e. tan ln cos. cos sin cos ln.. e e 9. arctan ln 7. e cos e sin e 9. e 9. arcsin. e e e e 8 ln arctan... sin cos y. (a) 98.7 gallons (b) 9.9 gallons (c) gallons
5 ALULUS WORKSHEET ON d 8. d. d 9. arctan d. e d. sec d.. e sin d. d ln d. arcsin d sin. d. d cos 7. sind. e d Answers to Worksheet on ln.. e e 9. ln sec tan. ln. cos arcsin 9. arctan ln9 esinecos. ln 7arctan.. arcsin. ln. e
6 ALULUS B WORKSHEET ON cos sin d 7. cos d. d 8. d 9.. sin ln d e sin d. arcsin d. d d.. sin cos d. d. cos d Answers to Worksheet on sin sin. ln arctan. cos sin cos 9 7. arcsin. sin. ln arctan 7. sin sin ln 9 9. e cos e sin. arcsin..
7 ALULUS B WORKSHEET ON sec tan d. 7. sin cos. tan sec d 8. sec 7 tan 7 d. cos sin d 9. sin cos d d. d. e cos d. sin d. cos d. arcsin d. cos cos d Answers to Worksheet on sec. or tan tan tan 8 8 tan. or sec sec sec 8 8 sin sin. 7. ln arctan. cos sin cos 9 7. arcsin 9 7. cos cos sec sin 8. e sin e cos.. sin sin 9 8
8 ALULUS B WORKSHEET ON d. cos d. d. tan. cos sin 7. sin sec d 8. d 9 d 9. d. d cos cos d. Given the region bounded by the graphs of y ln, y, and e. Find (a) the area of the region (b) the volume of the solid generated by revolving the region about the -ais. Answers to Worksheet on arctan sin sin.. sin cos sin 8 sec sec.. 7. sin ln 9. sin sin. (a) e (b)
9 ALULUS B WORKSHEET ON Evaluate. Do not use your calculator. cos d.. cos d 9. arctan d d.. sin ln d. d. d 7. d. 8 d. arcsin d 8. 9 d. e d Answers to Worksheet on sin cos sin 8. sin.. 8. sin sin ln. 7. ln 8 arctan 8. 9 arcsec 9. arctan ln. arcsin 8.. e
10 ALULUS B WORKSHEET ON d. sin d 7. arctan d. d. 7 d 8. d. d. d 9. e cos d. Given the region bounded by the graphs of y cos, y,, and. Find the volume of the solid generated by revolving the region about the -ais. Answers to Worksheet on ln. ln ln.. cos cos 8. ln ln. 7. arctan ln 8. ln ln arctan 9. e cos e sin.
11 ALULUS B MIXED INTEGRATION WORKSHEET.. ln d. sin d. tan sec d 9. d 9 9. e sin d d. 9 d 7. sin cos d. d 9. sin d 8. sin cos y arctan. Solve for y: d Answers to Mied Integration Worksheet ln... 9 arcsec. cos sin cos 8 sec sec tan tan. or. ln sin 8 9. ln 7. e sin e cos. ln. arctan ln9
cos 5x dx e dt dx 20. CALCULUS AB WORKSHEET ON SECOND FUNDAMENTAL THEOREM AND REVIEW Work the following on notebook paper. No calculator.
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Ex. Find the derivative. Do not leave negative exponents or complex fractions in your answers.
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