A) 0.74 B) 2.96 C) 8.89 D) 0.92

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1 Bous Assigmet Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Use a fiite sum to estimate the average value of the fuctio o the give iterval by partitioig the iterval ad evaluatig the fuctio at the midpoits of the subitervals. ) f(x) = x o [,7] divided ito subitervals (Roud to the earest hudredth.) ) A).7 B).96 C) 8.89 D).9 Estimate the value of the quatity. ) Joe wats to fid out how far it is across the lake. His boat has a speedometer but o odometer. ) The table shows the boats velocity at secod itervals. Estimate the distace across the lake usig right-ed poit values. Time Velocity (sec) (ft/sec) A) 7 ft B) 5 ft C) 7 ft D) 7 ft Use a fiite approximatio to estimate the area uder the graph of the give fuctio o the stated iterval as istructed. ) f(x) = x betwee x = ad x = 6 usig a upper sum with two rectagles of equal width. ) A).5 B). C).5 D).5 ) f(x) = x betwee x = ad x = 6 usig the "midpoit rule" with four rectagles of equal width. ) A) 69 B) 86 C) 5 D) 6 Use a fiite sum to estimate the average value of the fuctio o the give iterval by partitioig the iterval ad evaluatig the fuctio at the midpoits of the subitervals. 5) f(t) = - cos t o [, ] divided ito subitervals 5) A) - B) C) D)

2 Estimate the value of the quatity. 6) A swimmig pool has a leak. The leak is gettig worse. The followig table gives the leak rate 6) every 6 hours. Time Leakage (hr) (gal/hour) Suppose it keeps leakig 7. gallos every 6 hours. After losig 6 gallos the leak is fixed. Approximately how log did the leak last? Use the right edpoits to estimate the first 8 hours. A).89 hours B) 7.89 hours C) -9.8 hours D) 5.69 hours Use a fiite sum to estimate the average value of the fuctio o the give iterval by partitioig the iterval ad evaluatig the fuctio at the midpoits of the subitervals. 7) f(x) = x5 o [, ] divided ito subitervals 7) A) 97.6 B) 58.6 C) 8. D). 8) f(x) = 5 + si x o [, ] divided ito subitervals 8) A) B) + C) + D) 5 9) f(x) = 7 x o [-, ] divided ito subitervals 9) A) 6 B) C) D) Write the sum without sigma otatio ad evaluate it. ) k + k k = A) = 5 B) = ) C) = 8 D) = Fid the value of the specified fiite sum. ak ) Give ak =, fid. ) k= k= A) B) - C) D)

3 ) Give ak = -6 ad bk =, fid k= k= k= ak - bk. ) A) -7 B) 6 C) -9 D) 7 Fid the formula ad limit as requested. ) For the fuctio f(x) = 6x +, fid a formula for the upper sum obtaied by dividig the iterval [, ) ] ito equal subitervals. The take the limit as to calculate the area uder the curve over [, ]. A) C) ; Area = B) ; Area = 57 D) ; Area = - ; Area = Fid the value of the specified fiite sum. ) Give ak = -6, fid ak. ) k= k= A) B) -8 C) - D) 8 Fid the formula ad limit as requested. 5) For the fuctio f(x) = x+, fid a formula for the upper sum obtaied by dividig the iterval 5) [, ] ito equal subitervals. The take the limit as to calculate the area uder the curve over [, ]. A) C) ; Area = 6 B) ; Area = D) ; Area = 9 ; Area = 9 Write the sum without sigma otatio ad evaluate it. 6) (-)k si 7 k = A) -si 7 + si 7 - si 7 = B) -si 7 - si 7 = 6) C) -si 7 + si 7 - si 7 = D) -si 7 + si 7 - si 7 = - Fid the average value of the fuctio over the give iterval. 7) f(x) = 8 - x o [-8, 8] 7) A) B) 8 C) D) 6

4 Evaluate the itegral. 8) 9 x + x + 6 dx 8) A) 6 B) 6 C) - 6 D) - 6 SHORT ANSWER. Write the word or phrase that best completes each statemet or aswers the questio. Provide a appropriate respose. b 9) What values of a ad b maximize the value of (6x - x) dx? 9) a ) Derive a formula for the area of a circumscribed regular -sided polygo for a circle of ) radius r. MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Express the limit as a defiite itegral where P is a partitio of the give iterval. ) lim P (sec ck) xk, [-, ] ) k = - A) sec x dx B) ta x dx - C) sec x dx D) sec x dx - Fid the average value of the fuctio over the give iterval. ) f(x) = 8x o [, ] ) A) B) 8 C) 6 D) 6 ) y = x - 5x + ; [, 8] ) A) 8 B) 6 C) D) Fid the derivative. si t d ) dt du ) - u cos t - cos t A) B) - si t - si t C) cos t ( - si t) D) - si t

5 Fid the total area of the regio betwee the curve ad the x-axis. 5) y = ; x 5) x A) B) C) D) Evaluate the itegral. log 6) x dx 6) A) log - B) C) D) l l 7) t + t A) 7 6 dx 7) B) 5 C) 9 6 D) 5 6 Fid the derivative. x6 8) y = cos t dt 8) A) 6x5 cos (x) B) cos (x) C) cos (x) - D) si (x) Fid the area of the shaded regio. 9) 9) A) B) 9 C) D) 7 Solve the problem. x+ ) Fid the liearizatio of f(x) = 5 + ta t dt at x =. ) A) x + 5 B) 5x + C) x + 5 D) 5 5

11.7 (TAYLOR SERIES) NAME: SOLUTIONS 31 July 2018

11.7 (TAYLOR SERIES) NAME: SOLUTIONS 31 July 2018 .7 (TAYLOR SERIES NAME: SOLUTIONS 3 July 08 TAYLOR SERIES ( The power series T(x f ( (c (x c is called the Taylor Series for f(x cetered at x c. If c 0, this is called a Maclauri series. ( The N-th partial