In the following exercises, given that
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- Q3. Find the cosine series for f(x) = 7 – x in the interval 0arrow_forwardObserve the function X f(x) = (1+2x)² In order to find the power series for this function, complete the following steps: 1 1-x a. Start with the series Σ. Replace x with (−2x) in this series and k=0 write the corresponding power series for = 1 1+2x b. Take derivative of the series from part (a) above and relate it to the power series for the function 1 (1+2x)²· c. Multiply both sides of the resulting series from above with x, and obtain the series for Write the first four non-zero terms of this series. X (1+2x)² d. What is the radius of convergence for this series? What is the interval of convergence?arrow_forwardDifferentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between the two series.arrow_forwardWhat function would you take the derivative of to find the Maclaurin series of the function f(x) = 4xe**? Sorry, that's incorrect. Try again? Basicarrow_forwardGiven f(x) = x² ,0 < x < 3, a) sketch the function during the period. b) Express f(x) as a half-range sine series in 0arrow_forwardExpand f(x) : = 5x? – 38x + 68 as a power series around 4. f(x) = (x – 4)°+ || (x – 4)+ -21 help (numbers)arrow_forwardFrom the following statements, choose the one(s) that are true. OA. The function f(x) = can be represented by the power series (- 1)"2"x2. 1+2x O B. The function f(x) = 1 can be represented by the power series 1 2+2x 2 OC. x"+1 00 The function f(x) = In(1+ x) can be represented by the power series O D. The power series Ln = 0 n! converges only when X=0 and has a radius of convergence of R=0. OE. The function f(x) = In(1- x) can be represented by the power series * n+1 OF. The power series *n! xn converges only when x=0 and has a radius of convergence of R=0.arrow_forwardConsider the function f(x) = 2 tan ¯¹(x). a. Differentiate the Taylor series about 0 for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative.arrow_forwardLet f(x) = 1 + x 1 X Find the power series representation for the function f(x) by completing the following steps: a. First, express the fraction 1¹ as a power series. = X b. Now, express the fraction as a power series. 1-x 1+x x c. The function f(x) 1-x 1-x + 1 is the sum of the two series from parts (a) and (b). Express the function f(x) as a power series. d. What is the interval of convergence and the radius of convergence for this power series?arrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
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