Question

-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use the binomial expansion definition to write the expansion for f(x) (1-2, 4. Parametric and Polar Forms (a) Convert these parametric equations to Cartesian form and sketch the curve: 2. t i. r(t) = t + 1, y(t)-2t-1for 1 ii, r(t)-5cos(2t), y(t)-2 sin(2), π/4S t t2-+1 at the point (-1, 1). 3T/4. 3r/4. (b) Find the equation of the tangent line to the parametric curve r(t)-+2t, i) - (e) Find the are length of the parametric curve r(t)-cosl2t), () -3 sin(2) for O sts (d) Sketch these polar curves: r= 1-cos(θ) i, and below by the -axis. (e) Find the area enclosed above by the polar curve re

Answer 1

Solst on of (0, 3) ale at ta Clt ct t-3t 2t+2 dy/dt 2 cn dt dx y-3 SA Cm

alt 3 i alt dlh ru (毛 I P