In the following exercises, given that
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- Q2. Find the convergence interval and radius of the series : Σvn (2x+5)" n=1arrow_forwardFind first two terms of the Taylor 3 d) ( series centered at a = 2 of the function f(x) x+ 2arrow_forwardbe the first three terms of the binomial series to approximate f(x) = 1 at x = 1/2. Then find f(¹/2) √1-X using a How clase was your approximation? calculater.arrow_forward
- Find the first five non-zero terms of power series centered at x = 0 for the function a representation below. x³ f(x) 1+ 3x Answer: f(x) What is the interval of convergence? Answer (in interval notation): = + = + + +..arrow_forwardUse the Root Test to determine if the series converges or diverges 1 (-1)"2n en? (2n2 – 1)" n=1arrow_forwardFind a power series for f(x) = In(1+ x). Hint: In(1+ x) is one antiderivative of (whose 1+x power series was listed in the video). Calculate the first few terms to help you identify the correct answer from the options listed below.arrow_forward
- Use the fact I a", find that the exponential function the series presentation (using the E notation) for the n=0 following functions: (a) g(a). ce dæ 9(x) = n=0 [The constant C is already written you). 00 h(x) = Σ n=0 DCFC 2872-DE42-D42D-FC70 FC76-51E35 AAAD57 5.00-6.10 PDT $21 Mini 3 09 021 5:00-6:10 PDT Provided to Jo ibute) JodM151 S21 MinTest3 09/Ap021 5.0010 PDT Provided to Jonathan J sharo/distribute/post/uploaO M151 S21 MiniTest3 09/Apr/2021 5:00 0 PDT bute/post/npload M151 1 MiniTest3 09/Apr/2021 5:00-6:10 RDT ovidedo Jonathan Jaimez-Menes peorde M151 S21 MiniTes ONApr/25:00-6:10 PDT 151 $21 MiTest3 09/Apr/221009OP niTest3arrow_forwardSomeone else gave the wrong solution,arrow_forwardUse a geometric series to represent each of the following functions as a power series about x = 0. Find the interval of convergence. a. f(x)= 5 2-X b. g(x)= 7 X-3 00 www a. The power series representation for f(x) is Σx". n=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.) b. The power series representation for g(x) is Σx". n=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)arrow_forward
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