4. For the function f(x) find the power series representation and its interval of (1 – 4x)² convergence.

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Q: Ax)

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Q: 3. For what values of x , does the series, 1-«-4)+ (* - 4)° --4). .... converge ?Find the ........…

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A: Consider the series ∑n=1∞xlnn We have to find positive value of x for which the given series is…

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A: The given series is, ∑n=1∞n2 sin nx3n+x2

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A: To find a power series of fx=2x1−x2

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Q: b), Find the interval of convergence of the power series ) -(x – 2)". 2n+1

A: I have used the definition of interval of convergence

Q: 3. For what values of x , does the series, 1-(x- 4)+ - (x – 4)* --(x - 4} + . + 1 (x – 4)² 4 1 (x –…

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Q: Find the radius of converges and the interval of convergence for the given power series. (х + 1)" 6º…

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Q: Note that you only have one chance. The power series of sin(x) at x= is given by k=0 (2k+1)! k=0…

A: Given Power series of  Sinx at x=π2

Q: Find the radius of convergence and interval of convergence of the series ;(-3)x* -o vn+1

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Q: (3x – 4)* is - The radius of convergence of the series 9k k=0

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Q: 4. Find the power series representation centered at 0 for f(x) = 8x 2+x³

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Q: 2 Represent the function as a power series f(x) : (1 – 7æ)2 n=0 e radius of convergence R

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Q: Find the interval and radius of convergence of the power series (x – 5)k k2 k=1

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Q: E(-1)* sin () i=1

A: Given : ∑i=1∞ -1isinπn

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Q: Expand f (x) = 2/(4 − 3x) as a power series centered at c = 0. Determine the values of x for which…

A: Given: f(x)=24-3x Simplify the expression. f(x)=241-34x=1211-34x…(1) Series for 11-x is:…

Q: 2x Find the power series representation of the function, f(x) = and determine its interval of…

A: Here the given function can be written as:

Q: Find the interval and radius of convergence of the power series (x + 1)½ k=1

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Q: Determine the radius and interval of convergence for the power series 3k (x – 9)*. k! k = 0 The…

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Q: The series ∑Cn(x+9)^n converges at x=−4 and diverges at x=−17.

A: We know that if the power series ∑ n=1∞an (x-b)n is convergent at x=a, then this series is…

Q: 5) Find the first five non-zero terms of power series representation centred at x = 0 for the…

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Q: B) Find the series' interval of convergence of E (tan-1x)" n%3D1

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Q: Find the interval of convergence of the series. (x-5) 5n+1 n=0

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Q: 3. Consider function f(x) given by the series 8∞ f(1) Σ- 2π)" n=0 Find a power series for f'(x) and…

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Q: 1. For this problem, you will apply either Root test, or a comparison test, or the nth term test for…

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Q: Find the interval of convergence of the series. (3x)" * Σ n2. 10" n=1

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Q: 4. Consider the following function: So, sin rx, 0 16k2 k=1 1 - -

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Q: 4 Represent the function as a power series f(x) = (1 — 2г) n=0

A: We know that  (1-x)^n = 1+x + x² + x³ +........ Using this we can solve given problem

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Q: The radius of convergence for the power series F(x-3)

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Q: Whar is the Taylor series representation for f(x)=ln(1+4x) and the interval of convergence?

A: we know that Replacing x by -4x , we get

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Q: 4 3) Let f(x) x2+4 Find a Power Series for f(x) centered at c= 0 and its interval for convergence

A: Please see the explanation below

Q: Given the power series Σ (x+ 2)" n =0 2" Find the "Interval of Convergence" for the series.

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Q: 4. If > Cn (T + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: The given power series is cn(x+2)n , n from 1 to infinity.

Q: Find the radius of convergence and interval of convergenc of the power series. 17. E (-1)"4" x" yn…

A: