WebThe function f(x) = 3x arctan(8x) is represented as a power series 00 f(x) = Σ cnx". n=0 Find the first few coefficients in the power series. Co = C1 = C₂ = C3 = C4 = Find the radius of convergence R of the series. R = Hint: Notice that d dx - -arctan(8x) = 8 1+64x²' , SO 1 ³/₁ 8 1 + 64x² Can you find a power series representation for a ... WebFind the function represented by the following power series. ∑n=0∞ (−1)n4nx2n This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer Question: Find the function represented by the following power series. ∑n=0∞ (−1)n4nx2n Show transcribed image text Expert Answer
How to Find the Interval of Convergence for a Power Series
WebFind step-by-step Calculus solutions and your answer to the following textbook question: Find the function represented by the following series and find the interval of convergence of the series. (Not all these series are power series.) $$ \sum _ { k = 1 } ^ { \infty } \frac { ( x - 2 ) ^ { k } } { 3 ^ { 2 k } } $$. WebPower series (Taylor, MacLaurin, geometric, in general) are useful for estimation. While that doesn't sound too exciting, it is apparently extremely useful in analysis, physics, and engineering, for models and differential equations that are difficult to evaluate … 0^0 is kind of undefined, so the only way to evaluate it is limits. You've got lim x->0 … rtt records
Solved The function is represented as a power series …
WebSorted by: 1 I think you have made an error in finding the general term. The geometric series ∑ n = 0 ∞ 8 ⋅ 6 2 n ⋅ x 2 n evaluates to 8 1 − ( 6 x) 2 which is not 8 ( 1 − 6 x) 2. Instead, start with the following well known series: 1 1 − y = ∑ n = 0 ∞ y n. WebThis calculus 2 video tutorial provides a basic introduction into the representation of functions as power series. It explains how to represent a function a... WebFirst, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. For example, … rtt ref count