4. consider the function: (1+x, -1 <1<0 f(r) = 2.x – 1, 0

Q: Q2/ Find the Fourier series to represent the function f(x) given by: -1 for f(x) = 0 for +1 for…

A:

Q: 6. Assume that the Fourier series of a function (x) on [-L, L] converges to f(x). (a) Derive the…

A: Given- Assume that the Fourier series of a function fx on -L, L converges to fx.  To find-  Derive…

Q: Find the Taylor series for f(x) = r'e+2) about the point r= 0.

A: Taylor Series: The Taylor series of a function fx about the point x=x0 is…

Q: . consider the function: [1+x, | 2.x – 1, 0<x <1 -1<1<0 f(1) = (i) Find the Fourier Series of f and…

A: We are given a piece-wise defined function, and we have to find its Fourier series expansion.

Q: 2. Find the Fourier series of the given function f(x), which is assumed to have the period 2L. f(x)…

A:

Q: 23// Expand f (x) = –x – n , -n<x< 0 in a half range sine series and Find its Fourier series

A:

Q: 4. consider the function: [1+x, -1 < x <0 f(x) = 2л — 1, 0<г <1 (i) Find the Fourier Series of f and…

A: The given problem is to find the Fourier series of the given function and check the convergence in…

Q: M=2 2. Find the value of an (n + 0) in the Fourier series expansion of the functions f (x) = sin(Mx)…

A:

Q: 4. Find the Fourier series representation of the function: -1<1<0 (t) = {-. *-1, 0<1<<1 which is…

A:

Q: Q2: Find the Fourier series corresponding to the function [ーk -くX<0 f(x)%D- 0<xく

A:

Q: Q2: Find the Fourier series corresponding to the function -k -n<x<0 S(x)3D k 0<x<T

A:

Q: Q5): Determine the Fourier series of the function f(x) = 1 - x² in the interval [-1, 1].

A:

Q: 1. Given: f(x) = 2x – 5,0 <x< 10 %3D Find the FOURIER SERIES of the EVEN EXTENSION of the given…

A: Fourier series

Q: (iii) At x = 0, the Fourier Sine Series of 2x – 2, 0 (A) –2 (В) —1 (C) 0 (D) 1

A: The given problem is to find the Fourier sine series of given periodic function and also to find  at…

Q: 4. Consider the following function: -I – 2, -2< < -1 f(1) = {r, -1<r<1 2-1, 1<r<2. (i) Sketch the…

A:

Q: 2: Find the Fourier series of the function for n >t >0 for 2n > t > n 2 f(t) = { , } -2

A:

Q: 3. Consider the function f defined by f(x) = b, 0 <x < L. i) Extend f as an odd function and find…

A:

Q: 2) Obtain the Fourier series expansion of the below function, f(x) = {2(k – x), 0, 0 <x<n %3D n<x<…

A:

Q: Q3. Find the Fourier series of the given functions f (x) which are periodic with period 2n and…

A: A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines…

Q: B/ Find the Fourier series of the function f (X) = x +n within the range -n < x < n

A:

Q: (b) At x = 0, the Fourier series of x - 2, -1 <x S 10, converges to: (A) -2 (B) –1 (C () The colut.

A:

Q: 5. consider the function: | 2.x + T, -T < x < 0 f(x) = T - x, 0 < x < T (i) Find the Fourier Series…

A:

Q: 1. a) Obtain a second-degree polynomial approximation to f(x) = (1+x)¹/2, using Taylor series…

A: Will obtain second degree polynomial approximation by using Maclaurin series and will find the bound…

Q: Find the Fourier series expansion of the periodic function of period 2 t f (x) = x, -n<x<n 1 Hence,…

A:

Q: Compute the Fourier cosine series of f(x) = 1+ x, 0 < x < a if ƒ(x +2x) = f(x). Sketch both the…

A: To calculate the Fourier cosine series of below function. fx=1+x,0&lt;x&lt;π

Q: Q2: Find the Fourier series of the function. if – n<t < 0 2 r(t) = r(t + 2n) = r(t) if 0<t <n 2 --

A:

Q: 1. Given: f(x) = 2x – 5,0 <x < 10 Find the FOURIER SERIES of the EVEN EXTENSION of the given…

A: Fourier even series

Q: A. Find the Fourier series expansion for: f(x) = x +- -n SxS T 4

A: We will expand as shown below

Q: Q2: Find the Fourier series of the function. f(1) ={ } for n>t >0 for 2n >t > TI 2 } -2

A: Fourier series

Q: b) Determine what the Fourier sine series of the function f(x) = { 2x-3 for 0 < x < 1 for 1≤x≤4…

A:

Q: 5. (a)Find the Fourier sine series for f(x) = x³ – n²x on the interval [-7, T]. (b) By plugging in a…

A: For (a), We need to find the Fourier sine series for the function, f(x) = x3 - π2x on the interval…

Q: Q4) A. Find the Fourier series of the periodic function -K when -n < x < 0} K when f(x) = *, and…

A:

Q: 2. (a) Find the Fourier series for the function f(t) = t² on the interval [-7, 7].

A: Given the function  ft=t2, -π,π

Q: 1. Find the Fourier Series of the function: SO, [0, -7< x< 0 f(x) l1, 0 <x< T

A:

Q: 4. Consider the following function: -I – 2, -2 <I<-1 f(1) = { T, |-1<r<1 2 r, 1< «< 2. (i) Sketch…

A: f(x) is continuous so Fourier series converges to f(x) at every x  Using parseval idetity for second…

Q: Find the Fourier series of the function f(x) periodic with period 2n 0<x<T f(x) = {10, I<x< 2n' and…

A:

Q: Q1 Let ø(x) = x² for 0 < x < 1. • Calculate its Fourier sine series by odd extension; • Calculate…

A: Solution a) Given that ϕx=x2 for 0≤x≤1. Odd extension of ϕ(x) is  ϕx=x2, 0≤x≤1-x2, -1≤x≤0 Fourier…

Q: 2. Determine the FOURIER COSINE series of f (x) = 2x2 in the interval 0 < z < T.

A:

Q: (a) Find the Fourier series of the function (x) = 1 – |x|, -2 < x< 2 (b) Hence prove that 1+

A: Given : function         fx=1-x  ,  -2&lt;x≤2 (a) To find : Fourier series of the function above (b)…

Q: 5. (a) Find the Fourier Series of the function (x) = 0 (x) = nx- x if 0< x< n. if -n < x < 0 (b) Use…

A:

Q: Q2. Find the Fourier series for the function f(x) = ›>-6 for for 0<x<π π < x < 2π

A: Sol

Q: Q4: Find a Fourier series of the function. F(x) = 1 - 3 x² in the interval - A<X<T

A:

Q: 1 f(2): 1 3 Find a Taylor series for f which is convergent in |2 – 1| < 1.

A:

Q: Q6: Find the Taylor series generated by f(x)=x°sin(8x) at x=0.

A: Given function is f(x)=x3sin8x. Since we to find the series about origin therefore we have to…

Q: 1. Determine whether the Fourier series of the following functions converge uniformly or not. Sketch…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Consider the function f(x) = cos(2x). %3D 1. Find the Taylor series for f(x) at x = T.

A:

Q: (b) Obtain the Fourier series expansion of f(x) = x sin(r) on [-Ħ,]. Use the series to deduce 1 1 1…

A:

Q: i) Consider the function f(x) = π-x, 0<x< T. a) Extend the function in an odd manner, and sketch the…

A: Since there are multiple parts, so find the solutions of first two parts (a) and (b).

Q: 1.1. Compute the Fourier series for f(x): f(x) = {, - 2 <x<0 0<x<2

A:

Q: Find the fourier series expansion of the periodic function f(x) = e², -a < I < 7, (1 + 27) = f(r).…

A: