University:
Rensselaer Polytechnic Institute
Course:
MATH 1020 | Calculus II
Academic year:

2021
Views:

473

Pages:

1
Author:

Sidak C.

Calc II Exam 3 Review Saturday, November 11, 2023 13:24 Sections 10.8, 11.1-11.4, 12.1 (+ dot product) 10.8) Tn (x) = f(c)+f(x-c).....(x- Taylor Polynomial centered at x=c of f(x) Ex: Find MacLaurin Series of a) f(x)= ex a) h(x)=e b) g(x)= 2023 x.ex Taylor Series b) 2023 2023-1 i! L jo j! Mac Lavrin Series (1:0) ILF-11M] CLE): (x(t), y(t)) coordinates x and y changing in time (CCE)) Ex: x(t)=2t to y(6)=4+ ( 10)=(0.0) (11)= (2,4) ( L2)= (4.16) Parametric Equation for Unit Circle Iconier at 10,0)) t-3 x(t)=2t y(t)=4t ((3) (6,86) Area sin't+ cos't=1 y(t)=3cost sin't cos't Ex: Para. Eq, for A: Jo fuidx Syltix x' (4) dt a) CLE)=(2sin(34), 200s (84)) 06 Ex: Find the length of the path b)(4)+(1+lmet), In (108) OCT a) x(t)= 6c0s(3+) 9(+)-6sin(34) b) x(6) + LS (34) 36m²(24) 4 y(t)= f(x) Slope of Tangent line at CLE) Arc Length dydat Ex: (C): (24), 44): dy Bt at 2 20 al t=2. dx bt 3t 15/36 (cas (2) + sin(86) do Speed Alony Path Ex: Determine speed along 8: (24', 81') at to2 5: √(be) (164) (24)+(42) 40 mls Surface Area SA 2Sylt + ly Lay dt Ex: Find the SA of (14) (4, 1) about dus get'dt -axis for ostel. Polar Coordinates Rect Polar Polar Rect Ex: P(3,4) Polar. P+ (Br) Rectangular P. Lx,y) Ex XIL Baston() yersin Bi arctom() Ex convert ex 16-riose into polar word. triostring): Ing. Arc Length (Polar) Area (Polar) Ext sin20 OSOS Ex: sine f(৮) de (e) sine F'(B) cos 12.11 Standard Basic Vectors in IR Dot Product The dot prodect of vocabies and wreniy.20 arbest (k k is odd-onse with e petals kis oven-rose with 24 petals Practice Problems Spring 2023 (Whole Exam Q1 a) x*46+6, you2+3 44-x-6 y=12613 y=3x-18 +3 LS-VER] E+ (725.6 Recr @2] a) (r.)= (2.) vw-63064=1 8237 5(2)+9(1) Acute .ws and and we are l 2049-24 24) 4.1) ((x)=e" f(0)=1 2(x):12 2 f'(x) Be f'(0)3 9x27x 2 6 3 1"(x) 9e" f"20)=9 25 x²+(y-1)=1 x²-42=4 x²+y²-2941=1 rcos'-r'sin' rosessing: 25 x225 -2y = 0 r-rsin'in 4.2) f(x)=e 25 25 -2n8:0 2rain r=2 tine b) r(t) (6403,8t) 06652 JA: J√36+64 dt 10+/ 701 = 99.01 20 rsin (46) 14:48 petals (24) A 9:177.4 3.3) 18+ 9) 5llull+9 19

Calculus II Exam 3: Review

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