n(x – 4)" 22n (2n – 1) Given the power series f(x) = >) n=0 Find f(2021) (4), the 2021-th order derivative of f evaluated at x = (Leave your answer in fraction form, and do not simplify.) = 4.
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Need some help with this. Do not simplify. thank you!
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- 6). Evaluate ∞ n = 0 (−1)n 2n + 1 as 1 0 f(t) dt where f(x) = ∞ n = 0 (−1)nx2n = 1 1 + x2 by identifying it as the value of a derivative or integral of geometric series. please show step by step clearly .Vv Express the function f(x) = a ln(1+cx) in power series form. Then evaluate the series at x = 0.127 using the first five terms of the series if a = 15.6 and c = 2.4. f(x,y)=e^x arctan y ; function up to terms containing third-order derivatives. (x0,y0)=(1,1) Open the Taylor series at point.
- f(x)=(3x+1) . a] Find the Taylor series expansion associated with f centered at 2.b] What is the largest interval on which the Taylor series expansion associated with f converges back to the function. Justify your answer as clearly as you can.Modify the power series ln ( 1 + x ) = x − x 2/ 2 + x 3/ 3 − x 4 /4 + x 5/ 5 − … to find a power series for ln ( 1 + x )/ x. Then use your power series for ln( 1 + x) /x to find the power series of the antiderivative ∫ ln ( 1 + x )/ x d x.(a) Find a power series representation for the function.f(x)=2/(19+x) (b) Determine the interval of convergence.
- 9). Given that 1 1 − x = ∞ n = 0 xn, use term-by-term differentiation or integration to find a power series for the function centered at the given point. f(x) = tan−1(x6) centered at x = 0 f(x) = ∞ n = 0 (. ). PLEASES HOW STEP BY STEP CLEARLY .Find a power series representing an antiderivative of f(x) = e-(x^4) Use the power series to evaluate lim as x--> 0 of (e-(x^4) + x4 - 1) / x8Find a power series solution of the differential equation given below. Determine the radius of convergence of the resulting series, and use the series given below to identify the series in terms of familiar elementary functions.