CALCULUS BC ANSWERS ANSWERS ANSWERS ANSWERS
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERSSPRING BREAKSection I, Part A (no calculator)3x ! 22x 3(2 x 3)(3) ! (3 x ! 2)(2)f '( x) (2 x 3) 26x 9 ! 6x 413 2(2 x 3)(2 x 3) 2f ( x) 1.2.3.4.5.D!,x 421x(t ) " sin 2tdt ! cos 2t C2114 " cos ! C , C 32211x(t ) ! cos 2t 3221111x(0) ! cos 0 3 ! 3 32222v(t ) sin 2t ; t Cn!13" 2# )% & 3 ( 1 2 5n 0 '3It’s a geometric series w/ r !tan( x h) ! tan xas h " 0hf ( x) tan x f '( x) sec 2 x2and a 1.3f ( x) Ey x 4 from x 1 to x 55y ' 4 x L ! 1 (4 x3 ) 2 dx3D16.7.exx! 1 e x dx ln(1 e ) CBdy x ! y !1dxf (1) !2f (1.2) ! f (1) f '(1)(.2) !2 (1 2 ! 1)(.2) !1.6f (1.4) ! "1.6 (1.2 1.6 " 1)(.2) !1.6 .36 !1.24BC
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERS18.(2 )[4 2k 16 12] 5222k 20Dk 109.1f ''(6) !22f (7) ! f (6)11On the tangent line: f (7) ! 3 !So f (7) 27!6221But f '(7) f '(6) , so on the curve: f (7) 2 , so 2A2f (6) 3 f '(6) !x2 x4 x6 .2! 4! 6!x2 x4e x 1 x .2! 4!x 2 x3 x 4e ! x 1 ! x ! ! .2! 3! 4!x2x4x6e x e ! x 2 2 2 2 .2!4!6!2461 x !xxxxe e ) 1 .(22! 4! 6!10. f ( x) 1 D11. x 2 y 2 z 2dx dz dydz kdt dt dtdtdxdydz2x 2 y 2zdtdtdtdzdzdz8 6k 10dtdtdt6k 21k B3x 4 y 32f ( e) 5x2f ( x) ! dx 2 ln x Cx12. f '( x) 5 2 ln e CC 4f ( x) 2 ln x 4f (e) 2 ln e 4 6DSPRING BREAK
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERSy (3t 1)!113. x 4t t 2y ' !3 (3t 1)!2x ' 4t 2tx '' 2x ''(1) 2y '' 18 (3t 1)!3y ''(1) ! 9 "a (1) # 2, % 32 &14.18 18 43 64B88dx "dx!4( x 2)( x ! 2)!22 " dxx 2 x!2 !2 ln x 2 2 ln x ! 2 C"x2 2 ln15. y Cx!2 Cx 211 x2E16. f '( x) x ! 2! f is increasing except at x 2f '' 0 when x 2, f '' 0 when x 2f ''(!2) undef ! inflection pt17.!#E(x " 3)2nnradius of convergence 1x !3 1n 1!1 x ! 3 12 x 4(2 ! 3) 2 n1" n " n div(4 ! 3) 2 n1" n " n divD18. f ( x) cos !1 (x 2 )f '( x) f '( x) !11 ! ( x 2 )2!2 x1 ! x4(2 x )BSPRING BREAK
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERS2x19. y 2 ! 2sin y at (2,0)2dydy x ! 2 cos ydxdxdydy 2 ! 2 cos 0dxdxdydyD 2!2dxdxdy3 2dxdy 2 dx 311p div2n3n 1 # n ! 3nlimII. !% & 3.0 0 1 convn !" ( n 1)! 3nn!' (!20. I.n"e# e 1 convIII. ( %&! ' !II&III E221.f ( x) 9 x 3 3x ! 6!13f '( x) 6 x 36x13f'x22. 3 0f '(0) undefrel min at 0u0E4400" xf '( x)dx xf ( x) !" f ( x) dx ]04u xv f ( x) (4(!3) ! 8) ! 0du dx dv f '( x)dx !20!2x 2! cos ! y 2! sin !dy 2! cos ! 2sin ! dx "2! sin ! 2 cos !A23. r 2! at " "2!BSPRING BREAK
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERSdAdr 2! r24. A ! r 2dtdtdCdr 2!C 2! rdtdtdAdC 2dtdtdrdrD2! r 4!dtdtr 2125.1dxdx"0 x alim "!0xa lim [ln x ]a lim [ln1 " ln a ]1a !0a !00! DNE26.E( a ( x ! 2) ; annlimn !"n" 2n 1 # % an !1& 3n ! 1 'an 1 ( x # 2) n 1 an ( x # 2) n 2(n 1) 1 %n 1& 3(n 1) # 1 ' an ( x # 2))lim (n !"an ( x # 2) n# 2n 3 lim &' x % 2 1n !" 3n 2()2 x % 2 133 x%2 2So the radius of convergence is 3/2C2x27. f ( x) "t 2 ! tdt4f '( x) 2 4 x 2 ! 2 xf '(2) 2 16 ! 4 2 12ESPRING BREAK
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERS! x 1 "28. f ( x) sin # 2 % x &x 1 # x 1 #lim sin % 2 & sin % lim 2 &x !"' x (' x !" x ( sin 0 0A! horizontal asympotote y 0Part B (with calculator)176.!4f ( x)dx 2 and0" f ( x)dx !30441101" f ( x)dx " fdx ! " fdx !3 ! 2 !5444111" (3 f ( x) 2)dx 3" f ( x)dx " 2dxB 3(!5) 6 !977.graph of fabcdf ''( x) f '( x) f ( x)ef ''(b) !, f '(b) 0, f (b) 78.79.r 2! cos ! for 0 # ! # "!1A # (2" cos " ) 2 d" 17.45620f (3) 8 f '(3) 5lim f '( x) 5 Nox !3E80.h '( x) 2 f '( x)2 inflection ptsBBDSPRING BREAK
CALCULUS BC81.y e!x2" !xV ( e 2 0& 0.8863ANSWERS ANSWERS ANSWERS ANSWERS222#%% dx'A82.83.84.f continuoous on [a,b]A) NO B) NO C) YES D) NO E) NOf (3.0) ! f (2.8) 293.0 ! 2.8f (3.1) ! f (3.0) 30.53.1 ! 3.0f '( x) increasing so f '(3) 30dP KP( A ! P)dtdP KP(1200 ! P)dt400 K (200)(1000)dP 400When P 200 ,dt1K 500dP1 P(1200 ! P)dt 500CDCf ( x)Using L’Hopital’s Rule:x ! 2 ( x " 2) 2f '( x) limx ! 2 2( x " 2)Bf ''( x) 5 lim x!22285.lim86.a15 (!1)16 ( x ! 3)3015!30 ! 29 ! 28 ! .! 32 ! 31 ! 30( x " 3)f (30) (3) " 015!16!30! 15!ESPRING BREAK
CALCULUS BC87.f 4 ( x) esin xANSWERS ANSWERS ANSWERS ANSWERSerror for P3 !error 88.f4x4!esin1 0.0974!BR(t ) 2 1 5t 34Avg rate 12 1 5t 3 dt 14.691!40C89.f (a) 0f '(c) 0Bf (c ) ! f ( d ) 0f (b) ! f (a )f '(a ) b!a90.f n (0) (!1) nn 1(n 2)2nn!0# 2 "1f '(0) "1%& ( 3' 2 ) 3# 3 3f ''(0) 1% 2 &( 4 ' 2 ) 163 13 2a2 ' x 2 x16 2!321 131So f ! x x 2 ! x3 .2 3326091.g ( x) f !1 ( x)11g '(3) f '(3) 4BDSPRING BREAK
CALCULUS BCANSWERS ANSWERS ANSWERS ANSWERS392.f '( x) sin( x ) for 0 ! x ! 2max at x 1.465CSPRING BREAK
Mar 25, 2011 · CALCULUS BC ANSWERS ANSWERS ANSWERS ANSWERS SPRING BREAK Sectio
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AP Calculus AB Summer Homework Name _ Dear Future Calculus Student, I hope you are excited for your upcoming year of AP Calculus! . concepts needed to be successful in calculus. Please submit this packet during your second calculus class period this fall. It will be graded. . final answers MUST BE BOXED or CIRCLED. 2 Part 1 - Functions .
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Honors Calculus and AP Calculus AB Readiness Summer Review This package is intended to help you prepare you for Honors Calculus and/or AP Calculus AB course this next fall by reviewing prerequisite algebra and pre-calculus skills. You can use online resources to review the learned concepts as well as your class notes from previous years.
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Pre-Calculus . The Pre-Calculus End-of-Course assessment is designed to measure student proficiency of the Common Core State Standards pertaining to Pre-Calculus. This course-level assessment is provided to all students who have completed Pre-Calculus or related courses. EOC Assessment Aligns to the Following Course Codes: 2053 - Pre-Calculus
