In the following exercises, you can use the fact that =
1+x+x2 +...+ xn+... for -1<x<1. First,
find the power series for (a), then use differentiation and
integration to express (b) and (c) as power series. Find the open
intervals of convergence.
In the following exercises, you can use the fact that = 1+x+x2 +...+ xn+... for -1<x<1. First, find the power ser...
(a) Use differentiation to find a power series representation for Rx) = (20 + x)2 Rw = °C f(x) = ). n = 0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for Rx) = (20 + x | 0 - 0 n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 f(x) = (10 + x330...
(a) Use differentiation to find a power series representation for f(x) = (7+x)2 (-1)"(n+1)x" 72+2 What is the radius of convergence, R? R = 7 (b) Use part (a) to find a power series for - 17+)3 (-1) (n+2)(n+1)x" 2.71+3 n = 0 What is the radius of convergence, R? R = 7 (c) Use part (b) to find a power series for Rx) = x 2 413 As - O What is the radius of convergence, R? R =...
please answer both!!!
(1 point) Use the binomial series to find the first 5 nonzero terms of the power series centered at x = 0 for the following function and then give the open interval of convergence for the full power series. 1 f(x) = (5 + x)5 f(x) = + + + + ... + (Give your The open interval of convergence is: answer in interval notation.) (1 point) For the following indefinite integral, find the full power series...
please help
5. . 1/6 points ! Previous Answers SCalc8 11.9013 (a) Use differentiation to find a power series representation for (5 + x)2 f(x) n 0 What is the radius of convergence, R? (b) Use part (a) to find a power series for f(x) =--1 (5 + x)3 f(x)- n=0 What is the radius of convergence, R? (c) Use part (b) to find a power series for fix)2 (5 + x) f(x) =
5. . 1/6 points ! Previous...
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Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 5 x f(x) = ;- n = 0 Determine the interval of convergence. (Enter your answer using interval notation.) Find a power series representation for the function. (Give your power series representation centered at x = 0.) x2 f(x) X4 + 16 f(x) = Σ |(-1)" ) n = 0 X (a) Use differentiation to find...
(1 point) For the following indefinite integral, find the full power series centered at 2 O and then give the first 5 nonzero terms of the power series and the open interval of convergence. $(t) = /2 2. In(1+x) dx f(t)=C+ n=1 f(t) = C+ + + +... The open interval of convergence is: (Give your answer in interval notation)
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Use the fact that arcsin(x) = to find a power series representation of f(x) = arcsin (2.c).
Express the function as a power series, find the first 5
coefficients of the terms, and find the radius of convergence.
(1 point) The function f(x) = 2x2 is represented as a power series (1-4x) f(x) = Xcnx". Find the first few coefficients in the power series. n=0 Ci = C2 = C3 = C4 = C5 = Find the radius of convergence R of the series. R=
= xsin(x2) 6. Use the Maclaurin series you know for f(x) = sin x to find the Maclaurin series for g(x) Hint: It is not necessary to do any differentiation to do this problem.
= xsin(x2) 6. Use the Maclaurin series you know for f(x) = sin x to find the Maclaurin series for g(x) Hint: It is not necessary to do any differentiation to do this problem.