AP Calculus AB Exam Review Sheet B - Session 1

Transcription

1 AP Clcls AB Em Review Sheet B - Session Nme: AP 998 # Let e the nction given y e.. Find lim nd lim.. Find the solte minimm vle o. Jstiy tht yo nswe is n solte minimm. c. Wht is the nge o? d. Conside the mily o nctions deined y constnt. Show tht the solte minimm vle o nonzeo vles o. y e, whee is nonzeo e is the sme o ll

2 Sppose lim, lim, nd is not deined. Which o the ollowing sttements is mst e te? I. lim II. is continos eveywhee ecept t III. hs emovle discontinity t None o them I only c III only d I nd III only e I, II nd III I y, then lim y is c d e DNE Sppose is continos, t not dieentile t the point nd. Which o the ollowing sttements mst e te ot? I. lim lim II. lim III. lim does not eist I only I nd II only c III only d II nd III only e I, II nd III

3 AP Clcls AB Em Review Sheet B - Session AP 7 #6 Nme: Let e the nction deined y k ln o >, whee k is positive constnt. Find nd. Fo wht vle o the constnt k does hve citicl point t =? Fo this vle o k, detemine whethe hs eltive minimm, eltive mimm, o neithe t =. Jstiy yo nswe. c Fo cetin vle o the constnt k, the gph o hs point o inlection on the - is. Find the vle o k.

4 Which o the ollowing sttements ot the nction given y is te? The nction hs no eltive etemm. The gph o the nction hs one point o inlection nd the nction hs two eltive etem. c The gph o the nction hs two points o inlection nd the nction hs one eltive etemm. d The gph o the nction hs two points o inlection nd the nction hs two eltive etem. e The gph o the nction hs two points o inlection nd the nction hs thee eltive etem. Wht is the vege te o chnge o the nction given y 5 intevl [, ]? on the closed c d e 66 I sin, then cos sincos c 6 cos d sincos e 6 sincos

5 AP Clcls AB Em Review Sheet B - Session AP 5 # Nme: The tide emoves snd om Sndy Point Bech t te modeled y the nction R, given y t Rt 5sin 5 A pmping sttion dds snd to the ech t te modeled y the nction S, given y S t 5t. t Both Rt nd St hve nits o cic yds pe ho nd t is mesed in hos o t 6. At time t =, the ech contins 5 cic yds o snd. How mch snd will the tide emove om the ech ding this 6-ho peiod? Indicte nits o mese. Wite n epession o Yt, the totl nme o cic yds o snd on the ech t time t. c Find the te t which the totl mont o snd on the ech is chnging t time t =. d Fo 6 t, t wht time t is the mont o snd on the ech minimm? Wht is the minimm vle? Jstiy yo nswe.

6 A city is ilt ond cicl lke tht hs dis o mile. The popltion density o the city is people pe sqe mile, whee is the distnce om the cente o the lke, in miles. Which o the ollowing epessions gives the nme o people who live within mile o the lke? d e d d d c d d I is nction tht is continos o ll el nmes, then dt t d d e d c I the sstittion is sed, then d is eqivlent to which o the ollowing? d e d d d c d d

7 AP Clcls AB Em Review Sheet B - Session Nme: 6 # Let e the nction given y cos. Let R e the shded egion in the second qdnt onded y the gph o, nd let S e the shded egion onded y the gph o nd the line, the line tngent to the gph o t =, s shown ove. Find the e o R. Find the volme o the solid geneted when R is otted ot the hoizontl line y. c Wite, t do not evlte, n integl epession tht cn e sed to ind the e o S.

8 I the e nde the cve ove the intevl [k, ] is 5, ind k c. d.68 e.89 The e onded y the pol ollowing? y nd the line y is given y which o the 6 d d c 6 d d d e None o these I the cves o nd g intesect o nd nd i g o ll on,, then the volme otined when the egion onded y the cves is otted ot the -is is eql to d g d g d c g d d g d e None o these

9 AP Clcls AB Em Review Sheet B - Session 5 Nme: 7 # Fom B A pticle moves long the -is so tht its velocity v t time t is given y v t sin t. The gph o v is shown ove o t 5. The position o the pticle t time t is t nd its position t time t is 5. Find the cceletion o the pticle t time t. Find the totl distnce tveled y the pticle om time t to t. c Find the position o the pticle t time t. d Fo 5 t, ind the time t t which the pticle is thest to the ight. Eplin yo nswe.

10 A pticle is moving long the is with velocity o v t sint cost o t in mintes. Wht is the totl distnce tveled te ive mintes? c 8.5 d 9.87 e 9.56 A pticle is moving long the is with velocity o v t sint cost, o t. Wht is the mimm cceletion ove the intevl [, ]? cos 7 d cos sin 7 sin cos sin e I hve no ide 7 c cos 7 sin A pticle moves long the is with velocity given y v t sint. When t the pticle is t. Whee is the pticle when t? c d e On the loo