AP Calculus BC Series Multiple Choice Solutions

1. AP Calculus BC Infinite Series Multiple Choice

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33. 1993 BC 31

( (G+ が | em

If s, = asno

aXe ‘ny um
Im = (Stn) 内 ho IM “ 1
w う の ar Gum” vo 5 (Ain = 5

tm
bw SN lx ==)
vo (= = (wh ym) =!

,to what number does the sequence {s, } converge?

/ y100
(B) 1 (©) : (D) (=) (E) The sequence does not converge.

lols
iQ
Im

34. 1993 BC 43

The coefficient of x° in the Taylor series expansion about x = 0 for f(x) = sin(x?) is

1 1 1
2) 수 (B) 0 © bo (D) 중 (E) 1

35. 1993 BC 43

The coefficient of x° in the Taylor series expansion about x=0 for f(x) = sin(+?) is

1 1 1
で (B) 0 (©) 而 (D) > (E) 1

o $
Sh st Km + — +.
a yl El 6
SES に
gos Gl
fo .
3 * 6 ce
eee

el |

36. 1993 BC 45
o sE
If Sf) => (sin? x) . then f(1) is
k=l

(A) 0.369 (B) 0.585 (C) 2.400 (D) 2.426 (E) 3.426

37. Ea 3
2 x": ye ey exi
1993 BC 45 n

= Yr
If f(x)= Y (sin? À. then f(1) is
aw series
(A) 0.369 (B) 0.585 (C) 2.400 (0) 2426 (E) 3.426
, 다 ay
ko = (set) + C2) 60) + lle
—_ ーー ンジ Sex «À
Sin’ Get .
a 中 we Six À 오그
\ Hi
5 A aa 개 세
EE se
E. sax
unk
< tay

lo E
iQ
iD

38. 1988 BC 13

sin(2x) =
© Gar ore
①) Ss っ

an? (2x) (CE
a rt

39. 1988 BC 13

sin(2x)=
=
3!

5

E
ャ ーーー+ ォ ーー

3!

E (yaa
(2n-1)!

Era

( 2x

2!

340:

LK zxO® x

3!

4

(

an? 3?
u Ta

2n

++

(27-1)!

MEN er ¡EE

(2n)!

x
+
2n)!

(ES

2n-1)!

e ra

Sek = X7 * ST
sen- ay - y 4 6
8 er

St
Vide

e 3

40. 1988 BC 30

EN):
o He)

o 33)

(B)

(E)

41. 1988 BC 30

42. 1988 BC 38

0

What are all values of x for which the series > il converges?
1%

(A) -I<x<1 (B) -l<x<1

(D) -1<x<1 (E) Allreal x

(©)

-l<x<l

43. 1988 BC 38

으 0

What are all values of x for which the series ター — converges?
ne?

2 -l<x<l © -Isx<l

YO -Isxsl

区 -l<x<l All real x
nt
yee yet see SVE | alata! le moitie

y have Eve
> AAww オ <

A
a
へ

IS
io
m

e 1

44. 1988 BC 44

Which of the following series converge?

L 과 cpm

el 2n+1
= 1(3Y
工 . 一 | ニ

と + 2 )
El

m. 3
naz Mn

(A) Ionly

(B) Ionly

(©) only

(D) Land II only
(E) LIL and III

45. 1988 BC 44

Which of the following series converge?

ft Ser A $> proto 가 by he Att Suse Ter

n=l

Y, IL 주비 に ca Ame armani Cs (pesones, pai)

O ey 10 ㅅ germline ies wd. | 어 지리 1 to i} 09
© ig (A hb
Mur 5 - my ses In tue | |
„a “inn om x is: A Si 4-90 hill
Ionly „Web te 이
By Ionl 2 ey ES
(C) IT only er u Ee Luo)
D) Land II only
(E) LILandIll < 60 -7 DNE
Vide

e

46. 1985 BC 10

2 (eet
For -l<x<1 if f(x) = >) —=—
or ャ <1 if f(x) 之 7

, then f’(x) =

(A) > qe 4272

m=
e 5 ae)

n=l

© y ey” q
n=1

© Yen
n=1

© Fey»

n=l

47. 1985 BC 10

e n+l 2n-1
For -1<x<1 ff). A
=

2n-1

. then f’(x)=

a Noya E Ly

n=l

YA > Cp wet

n=l

の bed -
Á Lo る cy" gr aL
W 도 ents"

n=l
x 3 cently”

n=l

lols
iQ
Im

48. 1985 BC 14

Which of the following series are convergent?

(A) Ionly (B) Monly (C) IandIMonly (D) Hand Monly (E) LIL and II

49. 1985 BC 14

Which of the following series are convergent?

Jules. pam Po4 5 Comins

2 37 002
Y IL arte. homme Gres 새어
2 3 n
yl 5 A shell, aldo.
Jill. po +. alt: series 1. eauk > abs. Vela
— 3 Im 。%。 < の

(A) Ionly (B) only © Tand Monly (D) Tan Monty 08) LIL and Il

IS
ia
>

el |

50. 1985 BC 31

(x-1)"

の
What are all values of x for which the series >
n

n=l

(6) 0<%i<2 (D) 0= ェ <2 (E) 0<x<2

converges?

(A) -lsr<l ©)

51. 1985 BC 31 other Xe!

(x-1)"

っ
What are all values of x for which the series > converges?
n

mi
A CI. -lsxsl ES ©) xs M osxss
‘ ; 1
Im lecNW n 1 We sr" | a | =
neo nal ‘Tem + wy a . \

(xD"
DTA
O£X<T
GE

delia u compete hai
va O dut luymanie

—

n

52. 1985 BC 42

The coefficient of x? in the Taylor series for e** about x= 0 is

1 1 1
(A) る (B) = © = (D)

Io

(E)

nile

53. 1985 BC 42

The coefficient of x? in the Taylor series for e* about x = 0 is

1 1 1 3 9
az ® = o; m5 OF
e 3
Pe A as
a! 3.

= >
8, (30
cha {eine E + Ed
而 3
y ee
a

= |+3ı+

sx
a
S a 4
He à

54. 1973 BC 16

a . sin! .
A series expansion of 다 호 15

(A)
(B)
©
3 58
(D) Lgl phy
t 21 4! 6!
Sing a
(E) ニャ ーー ニキ

55. 1973 BC 16 3 ゼ

; sin’ .
A series expansion Of is

> 4 s
@eee. Mt,
이 위 7 t + tal 4:51
Aa 2 4
a Son 过。 党
이긴 xn 51
w ¡e
3! 의 7!

56. 1973 BC 19

Which of the following series converge?

ioe Ln y 때 yl
nal が nl" ma vn

(A) Ionly (B) II only (©) TandI only 00) land Monly (E) LIL and Il

57. 1973 BC 19

Which of the following series converge?

o = au
Air KW rt #29

n= 9 nl” n=l

(A) Ionly (B) Monly (C) IandIIonly (D) IandJIIonly (E) LIL and HI
ae pres ヤッ 4 바트
고 | pures ? =1 dnveguo

u ， dl Aland, Y
D. ake in cae aad
ca be ro! /

IS
ia
>

el ]

58. 1969 BC 28

っ nn
ER; E A B 4
> eu is the Taylor series about zero for which of the following functions?
no 7

(A) sinx (B) cosx (©) e (D) e* (E) m+y)

59. 1969 BC 28

っ non
pris = is the Taylor series about zero for which of the following functions?
n=0 UN

(A) sinx (B) cosx © e OB Œ) Ind+x)

o \ て
て 3
ase
(= Ae EA?
E 3
3 E -x LX. As.
Ms A = “Xt
ee 000 cvs | Ey
À 1 à
と A ー < lex Xd 4…
osx < en 으 애 = NG
s Pe Voy KK EE
A X x

60. 1969 BC 32

For what values of x does the series 1+ 27 + 37 +4 +---4n*+--- converge?

(A) No values of x (B) x<-l (C) x2-1 (D) *>-1 (E) All values of x

61. 1969 BC 32

For what values of x does the series 1+ 2° +3" +4" +--+" エー converge?

(A) No values of x x<-l (©) x2-1 (D) x>-1 (E) All values of x

x 2 a 24
à + ae

wha © à
wee A
Aa

n:

<
ia
>

el ]

62. 1969 BC 45

(x+1)* ：
記

2
The complete interval of convergence of the series >
k=l

(A) 0<x<2 (B) 0<x<2

(D) -2<x<0 (E) -2<x<0

15

(©)

-2<x<0

63. 1969 BC 45 de EXE CE Vr E A “eur

(x+ fy :
The complete interval of convergence of the series HL js
ka À

x O<x<2 Ww O<x<2 % -2<xs0

Y ~2<x<0 (E)) -2<x<0

tw ALE Aon
\ う ゅ (ey Lane is. (ge) e = be!
-l<xl< |
-1<X<0O

balk. eves a | Ses p> |
-! 시 기 Xs が __ ャ a p
Nat: a dar vi odos VÍ

2
LA = 0 k LT

lol<
iQ
Im