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15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered a...
2. Use the definition of Taylor series to find the Taylor series of f(x)=sin(2x), centered at ca. You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. 4
Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 2x² + 1 PX = (O 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.) Rx) = 2x f(x) = Σ n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)
Find the power series representation for g centered at O by differentiating or integrating the power series for f(perhaps more than once). Give the interval of convergence for the resulting series g(x) = In (1 - 2x) using f(x) Which of the following is the power series representation for gcentered at 0? LOA 28 Bit OC 1201 NI 883 NI The interval of convergence is (Simplify your answer. Type your answer in interval notation)
QUESTION 6 Compute the Taylor series of f(x)= sin 2x at Then show for the series above that linck; f(x) = 0 for each r QUESTION 7 Let f (x) =-x + 3, x E [0, 1] and let P be a partition of [0,1] given by 1 2 n-1 Calculate L(P) and U(P) and prove using these summations that f is Riemann integrable on [0, 1]. Also evaluate o f(x)dx.
Find the Taylor series for f(x) = sin(2) centered at 3. To help express the coefficients in a convenient way, it may help to define the sequence {on}no = {1,-1,-1,1,1,-1,-1,...}. What is the radius of convergence? Use Taylor's inequality to determine whether or for what values of x) the Taylor series converges to sin(x).
Find a power series representation for the function. (Give your power series representation centered at x = 0.) $(x) = 571 f(x) = { o n = 0 Determine the interval of convergence.
Find a power series representation centered at O for the following function using known power series. Give the interval of convergence for the resulting series. 2 f(x) 2+x Which of the following is the power series representation for f(x)? ΟΑ. Σ(3) OB. 2 ko OC. (-2011 OD. (-x?)" The interval of convergence is (Simplify your answer. Type your answer in interval notation)
15. . 16 . 17 Find a power series representation for the function. х f(x) (1 + 6x)2 f(x) = ( (-6).*- 1 nxt n = 0 x Determine the radius of convergence, R. R = 1/6 Evaluate the indefinite integral as a power series. t Vi dt 1 - 79 C+ Σ Σ( n = 0 What is the radius of convergence R? R= Use a power series to approximate the definite integral, I, to six decimal places. x3...
Find the power series representation centered at c = -3 for f(x) 2 x+5