Use the definition to find the Taylor series (centered at c) for the function. f(x) = ex c = 0

Q: Q4. Find the Fourier sine series for the function: f(x)= 0 for 0<x< 1/1 for 1/1/1<x<

A:

Q: For f (x) = /1 +2x. Find the the Taylor series centered at 1 by differentiating.

A: Given: centered at a =1.  The formula for Taylor's polynomial centered at x=a.

Q: Write the first three terms of the Taylor series for f(x) =Vx at a = 1. Show your reasoning

A:

Q: Find the first four terms of the Taylor series for xcos(2x).

A: first four terms of the Taylor series for xcos(2x).

Q: For f(x) = 4 on (0,t), find the Fourier sine series of f(x). Make sure to write the series.

A:

Q: Q2. Obtain the Fourier series for the function given in the diagram below f(x) 2 20 0 2T 3T X -2

A:

Q: for -π<x<01 04. Find the Fourier series for the function: ƒ(x)= for 0<x< T

A: Fourier series of the function

Q: Calculate the Fourier series of the function f(x) = x on the interval [−2,2].

A:

Q: Let g(x) = 4x sin(3x). Find the Taylor series for g(x).

A: Given,  g(x) = 4x sin(3x) ;

Q: Find the half-range sine series for the function f(t)=nt-t², in the interval 0<t<n.

A:

Q: I/ Find the Fowier Series for the periodic function shown bellow.

A: We will find out the required series.

Q: Let f(x) = √x. Find the Taylor polynomials P2(x) and P3(x) from your series above.

A: n

Q: 4. Find the Fourier cosine series for the function: f(x)= 1 for 0 for 0<x< 1/12 1 2 <x<1

A:

Q: Find the Fourier series for f(x) = -x, –1< x <1

A: