Chapter 5: Take Home Test

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1 Chapter : Take Home Test AB Calulus - Hardtke Name Date: Tuesday, / MAY USE YOUR CALCULATOR FOR THIS PAGE. Roud aswers to three plaes. Sore: / Show diagrams ad work to justify eah aswer.. Approimate the value of d usig a regular partitio of MIDPOINT retagles with =. (Sketh the futio & show the retagles you are usig.) Write your fial aswer i the lak... The veloity v (i m/s) of a rollig all at time t (i seods is reorded elow. Fid a upper ad lower estimate for the distae the all has traveled durig the te-seod iterval. Time (seods) 8 Veloity (m/s) *Show what you are pluggig ito your alulator for eah part. Upper:. Lower:. Calulate the sum to the earest thousadth: k k k.

2 Ch Take Home Part - No Calulator AB Calulus - Hardtke Name -. Multiple Choie: Selet the BEST aswer for eah statemet.. For a ostatly dereasig futio the value of a Left-Edpoit Riema Sum will e _?_.. A. higher tha the atual area B. eatly equal to the atual area C. lower tha the atual area D. lower tha the midpoit area E. oe of these. For a ostatly ireasig o-liear futio, the value of a Midpoit Riema Sum will e _?_.. A. equal to the defiite itegral B. equal to half of the area C. a regular partitio D. lower tha the sum of irumsriig retagles E. all of these. For a Riema Sum with partitio -oordiates at {8,,,, 9}, = _?_.. A. B. C. D. E.. For a Riema Sum with partitio -oordiates at {,,,, }, = _?_.. A. B. C. D. E. 8. Give partitio -oordiates at {8,,,, 9}, for a Midpoit Riema Sum, = _?_. 8. A. 8 B. C. D. E. 9. For ay Reima Sum over [, ] with a regular partitio ad =, = _?_. 9. A. B. C. D. E.. For a futio defied over [a, ], lim f ( i) is _?_, provided the limit eists.. i A. the derivative of f() B. the defiitio of f ()d C. a approimate value of the area uder the urve a D. equal to E. oe of these. If you estimate the area uder the urve f() = etwee = ad = usig suitervals of equal legth,. what is the largest value the approimatio ould have? A. B. C. D. E.. Estimate the area uder the urve f() = for. What is the value of the estimate usig four. retagles at the left had edpoits? A. B. C. D. E Let f( ) o the iterval [, ]. Let the iterval e divided ito two equal suitervals. Fid the value. * of the Riema sum i A. B. f if eah i * i is the midpoit of its iterval. C. D. E.

3 . d. A. B. C. D. E. oe of these For Prolems -8: Give f is itegrale over a losed iterval otaiig a, ad (i ay order); f ()d = ad a f ()d = m... f ()d = _?_.. A. m B. m C. D. E. oe of these a f ()d = _?_.. C. m D. E. A. B. m. f ()d = _?_. a A. m + B. m - C. m D. m E. oe of these a f ()d = _?_. 8. A. B. C. D. d E. oe of these = _?_. 9. d A. twie the value of B. egative C. oe-half the value of D. zero E. oe of these. If f() is a odd futio, the d f ()d is _?_.. A. twie the value of f ()d B. egative C. oe-half the value of D. zero E. oe of these f ()d. si d.. A. os B. os C. os + C D. ½ si + C E. oe of these se d. A. B. C. D. E. oe of these. si d. A. B. C. D. E. oe of these

4 . d. A. B. 8 C. 9 D. E. oe of these. d. A. B. C.. D. E. oe of these d. A. ( + ) + C B. ar ta + C C. ar ta D. ta C E. oe of these. e d. A. e B. ½ e C. ½ (e ) D. (e ) E. oe of these d = 8. A. - + C B. ½ - + C C. ar ta + D. l + C E. oe of these s ot d = 9. A. B. C. D. E. oe of these. For, A. + C B. 8. d =. d C C. C D. C E. oe of these =. A. 8 B. C. D. E. oe of these. If d, fid the value of.. A. B. C. D. E. oe of these. d =. A. ½ B. C. l D. E. oe of these

5 . Fid g ( ) give g() =. Fid w (t) give w(t) =. Fid s () give s(t) = ( ). The graph of a ar s veloity futio v(t) i mi/h is show elow..a. B. C. 8. Give the graph of a futio f elow. Lael the followig quatities from smallest (#) to largest (#) f() f ( ) d f ( ) d f ( ) d f ( ) d f ( ) d # # # # # A. f(-)= f(-)= f()= f() = f()= f()= B. C.

6 For Prolem : Give. Simplify k k ( )( ) k ad k k k ( ) (No TI-89! Ca you do it yourself?).. Write the epressio i Sigma otatio: (No eed to simplify, just rewrite the otatio.) Give d. A. Fid a umer that satisfies the olusio of the mea value theorem for itegrals.a B. Fid the average value of the give futio o the iterval. B.. Solve the differetial equatio give f " () = ; f ' () = ; ad f() =..

7 AB Calulus - Hardtke Chapter : Take Home Test SOLUTION KEY Date: Tuesday, / Sore: / MAY USE YOUR CALCULATOR FOR THIS PAGE. Roud aswers to three plaes. Show diagrams ad work to justify eah aswer.. Approimate the value of d usig a regular partitio of MIDPOINT retagles with =. (Sketh the futio & show the retagles you are usig.) Write your fial aswer i the lak... The veloity v (i m/s) of a rollig all at time t (i seods is reorded elow. Fid a upper ad lower estimate for the distae the all has traveled durig the te-seod iterval. Time (seods) 8 Veloity (m/s) *Show what you are pluggig ito your alulator for eah part. Upper:. Lower:. Calulate the sum to the earest thousadth: k k k.

8 Ch Review Part - No Calulator AB Calulus - Hardtke SOLUTION KEY -. Multiple Choie: Selet the BEST aswer for eah statemet.. For a ostatly dereasig futio the value of a Left-Edpoit Riema Sum will e _?_.. A. higher tha the atual area B. eatly equal to the atual area C. lower tha the atual area D. lower tha the midpoit area E. oe of these. For a ostatly ireasig o-liear futio, the value of a Midpoit Riema Sum will e _?_.. A. equal to the defiite itegral B. equal to half of the area C. a regular partitio D. lower tha the sum of irumsriig retagles E. all of these. For a Riema Sum with partitio -oordiates at {8,,,, 9}, = _?_.. A. B. C. D. E.. For a Riema Sum with partitio -oordiates at {,,,, }, = _?_.. A. B. C. D. E. 8. Give partitio -oordiates at {8,,,, 9}, for a Midpoit Riema Sum, = _?_. 8. A. 8 B. C. D. E. 9. For ay Reima Sum over [, ] with a regular partitio ad =, = _?_. 9. A. B. C. D. E.. For a futio defied over [a, ], lim f ( i) is _?_, provided the limit eists.. i A. the derivative of f() B. the defiitio of f ()d C. a approimate value of the area uder the urve a D. equal to E. oe of these. If you estimate the area uder the urve f() = etwee = ad = usig suitervals of equal legth,. what is the largest value the approimatio ould have? A. B. C. D. E.. Estimate the area uder the urve f() = for. What is the value of the estimate usig four. retagles at the left had edpoits? A. B. C. D. E Let f( ) o the iterval [, ]. Let the iterval e divided ito two equal suitervals. Fid the value. * of the Riema sum i A. B. f if eah i * i is the midpoit of its iterval. C. D. E.

9 . d. A. B. C. D. E. oe of these For Prolems -8: Give f is itegrale over a losed iterval otaiig a, ad (i ay order); f ()d = ad a f ()d = m f ()d = _?_.. A. m B. m C. D. E. oe of these a f ()d = _?_.. C. m D. E. A. B. m f ()d = _?_. a A. m + B. m - C. m D. m E. oe of these a f ()d = _?_. 8. A. B. C. D. d E. oe of these = _?_. 9. d A. twie the value of B. egative C. oe-half the value of D. zero E. oe of these. If f() is a odd futio, the d f ()d is _?_.. A. twie the value of f ()d B. egative C. oe-half the value of D. zero E. oe of these f ()d. si d.. A. os B. os C. os + C D. ½ si + C E. oe of these se d. A. B. C. D. E. oe of these. si d. A. B. C. D. E. oe of these

10 . d. A. B. 8 C. 9 D. E. oe of these. d. A. B. C.. D. E. oe of these d. A. ( + ) + C B. ar ta + C C. ar ta D. ta C E. oe of these. e d. A. e B. ½ e C. ½ (e ) D. (e ) E. oe of these d = 8. A. - + C B. ½ - + C C. ar ta + D. l + C E. oe of these s ot d = 9. A. B. C. D. E. oe of these. For, A. + C B. 8. d =. d C C. C D. C E. oe of these =. A. 8 B. C. D. E. oe of these. If d, fid the value of.. A. B. C. D. E. oe of these. d =. A. ½ B. C. l D. E. oe of these

11 . Fid g ( ) give g() =. Fid s () give s(t) =. Fid w (t) give w(t) = ( ). The graph of a ar s veloity futio v(t) i mi/h is show elow..a. B. C. 8. Give the graph of a futio f elow. Lael the followig quatities from smallest (#) to largest (#) 8 f ( ) d # 8 f ( ) d 9 f ( ) d # f ( ) d # f ( ) d f() # # A. f(-)= f(-)= f()= f() = f()= f()= B. C.

12 For Prolem : Give k k k. Simplify k. ( )( ) ad ( ) k k (No TI-89! Ca you do it yourself?) Write the epressio i Sigma otatio: (No eed to simplify, just rewrite the otatio.). Give d. A. Fid a umer that satisfies the olusio of the mea value theorem for itegrals B. Fid the average value of the give futio o the iterval..a B.. Solve the differetial equatio give f " () = ; f ' () = ; ad f() =..

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