3. Find the derivative of the series (-1)**'2" -x2n+3 n=0 n!

Q: Obtain the half-range sine series for the function f(x) = x² in the interval 0<x<3.

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Q: (sin z)2; 20 = 0 20

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Q: 1. Find the Fourier series of the function: f(x) = |x| in the period of -n<x<

A: Fourier series formulae: f(x)=a02+∑n=1∞ancos(nx)+bnsin(nx)a0=1π∫-ππf(x)dxan=1π∫-ππf(x)…

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A:

Q: Find the positive values of x for which the series > xnn is convergent. n= Is the function f(x) = >…

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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Q: where f(x) = 5 x^ by identifying it as the value of a derivative or integral of geometric series. as…

A: Given that: fx=∑n=0∞xn Which is the sum of geometric series. Derivative of the function is:…

Q: Find the coefficient of x10 in the power series of this function f(x) = %3D (1-3x)?

A: The solution is given as

Q: 1 Given that 5 x^, use term-by-term differentiation or integration to find a power series for the…

A: Given: The power series11-x=∑n=1∞xn. The function f(x)=ln(1+x2).

Q: Find the second derivative of f at x = 0 if the Maclaurin series for f(x) = 1-9x+16x2-25x3 + ...

A: We have to find derivative

Q: What is the power series for f(x)= 2/1+7x ?

A: we have been given the function  f(x)=21+7x

Q: 2- Determine the half-range sine series for the function defined by: x, 0 <x < 2 f(x)= 0, <x < T

A:

Q: Obtain a Fourier series for the periodic function f(x) defined as follows: 1- -1, when – n <x<0 1,…

A: We will answer only the first question as we don't answer multiple questions at a time. Please…

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

A:

Q: Find the first four derivatives with respect to x of y = In (1 + sin x). Hence, show that the…

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Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: Find the half-range sine series of f(x) = ex on [0, 1]

A: The half-range sine series of a function f(x) on an interval 0,a is given by, fx=∑n=1∞ bn sinnπxa…

Q: Find the first four terms of the Maclaurin series for f(x) = /2 sin( 3x+

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Q: Find Ln(0.98) by Maclaurian series F(x)=Ln(X+1)

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Q: 3. For what values of x , does the series, + converge ?Find the ........... first two derivatives of…

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Q: 4. Represent the function f(x) = as a power series centered at zero. %3D 5+x?

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Q: 2. Use differentiation to find a power series representation for f(x) = (1+x)²·

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Q: 3. Find the Maclaurin series for f(x). If the nth derivative of f at x-0 is given by * fla) (0) = (n…

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Q: Evaluate the infinite series by identifying it as the value of a derivative of a geometric series.…

A: Solution

Q: Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. n…

A:

Q: Verify F (1,1; 2;x) = –x¬ln(1 – x) By expanding each function in a power series about x = 0.

A:

Q: 2. Find a power series representation for the function. sin x f(x) =

A: given : f(x)=sinx/x we have to find its power series .this can be done using maclaurin series…

Q: ( Express the series x + 4)" as a simplified 2" n=0 rational function.

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Q: Which of the following is a power series about base point 0 for the derivative of f(x) = z²e-²?

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Q: Find a power series for f(x) = ln(1+x^4)

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Q: Obtain Fourier sine series and Fourier cosine series for f(x) = x3 in the interval [0, π].

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Q: 2 Obtain (a) the half-range cosine series and (b) the half-range sine series for the function 0. 0(…

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Q: If y =1+2x + 4x² + 8x +... i) Show that x= y -1 2y i) Find the interval in which the series is…

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Q: 1) Discuss an uniform convergent, continuous ,integral, derivative sinnx for a series E n?

A: Given the series as ∑sinnxn2 First, we will prove that the series converges for all real x, by the…

Q: use differentiation to find a power series representation for x^2/( x^4 + 81)

A: Given: Find the power series representation.

Q: 00 3x as a power series f(x) = >) Represent the function 2 + x n=0

A:

Q: If the derivatives of a function f(x) at a=6 are f^(n)(6)=(n!/8^n)(n/n+3)^n find the Taylor series…

A: First I have written the formula for Taylor series of a function at centered a, using that formula ,…

Q: Illustrate an example (with the answer) for the differentiation of power series of a function.

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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

Q: What are the values of x that make the next series convergent (sin(x))" n n=1

A: To find the values of x for which the fpllowing series converges…

Q: ex-e-* Find Maclaurin series for: 1. sinh x = 2

A: Find your answer below

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Q: Q1): use Binomial series to find the first four terms of the function: dx V1- x2

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Q: Find a power series for the function f(x)= (1-x^2)/(1+x^2)

A: From the given problem: fx=1-x21+x2   From the Power series:…

Q: Evaluate the indefinite integral using the series you found in problem 1₁ 1 1+x5 -dx

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Q: Ex. (4) fx) = 1; (0<x<x) =0 (7<x< 27)

A: