17. Find the interval of ocnvergence of the power series n(x – 3) 18. Write down...
Please write in clear solution. Thanks.
a) Find the radius and interval of convergent of power series on(x+2) . 31+1 [4 marks] b) Find the Maclaurin series for the following function: i. sin x [3 marks 11, cos x [3 marks] 2
(1 point) Find the interval of convergence for the following power series: n (z +2)n n2 The interval of convergence is 1 point) Find the interval of convergence for the following power series n-1 The interval of convergence is: If power series converges at a single value z c but diverges at all other values of z, write your answer as [c, c 1 point) Find all the values of x such that the given series would converge. Answer. Note:...
(1 point) Find the interval of convergence for the given power series. The series is convergent from x= , left end included (Y,N): to x = , right end included(Y,N):
Find the interval of convergence for the following power series.
Explain each step. X∞ n=1 x n 5 n √ n
5. Find the interval of convergence for following power series. Explain each step. n=1
Find the interval of convergence for the given power series. (2 - 4)" 00 n=1 nl - 3)" The series is convergent from 2 = , left end included (enter Yor N): right end included (enter Y or N): to C = CI" 10.2 Suppose that (14 + 2) n=0 Find the first few coefficients. Со = C1 C2 C3 C4 Find the radius of convergence R of the power series. R= 2 The function f(x) is represented as a...
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
7. (25) Solve the following problems. (a) Find the limit (b) Find the interval of convergence of the following power series 0O TL Tl n-1 (c) Find the sum of the following power series and determine the largest set on which your formula is valid n= 1 (d) Let f(x) = cosa. Find T6(2), the Taylor polynomial of f at zo = 0 with degree 6 (e) Calculate the Maclaurin series for the following functio f(x) = In
7. (25)...
3. Find the radius and interval of convergence for the following power series. (x-4)" 9 n=0
3.- Find the interval and radius of convergence of the following power series. 6'2" (a) (-1)" (x - 2)" (b) m3n 4.- Find the points of intersection of the pairs of curves. n=1 nel (a) r= 2 cose, r=1+cos (b) p2 = cos(26), r2 = sin (20)
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...