(1+x) Pn (x) dx = let Pn (x) be legendre polynomial of degree n>1, then, .a 2n +1 .b .C 1 2n +1

Q: a) Find a Taylor polynomial of degree 4 for f(x) = sin(x) expan- ded about xo = 0. ) Find the error…

A: Nothing

Q: - T < x < 0 0 < x < n' (-t, B. Find the Fourier series for the f (x), if f(x) = {,"

A:

Q: Q-2. Determine the values of x for which the function J (X) =$in Xcan be replaced by the Taylor 3…

A: We have to find the value of x as per given conditions.

Q: Given: In(1+ x) = > (-1)" -xn+1 if |x| < 1 n + 1 n=0 Use the third degree Maclaurin polynomial of f…

A: Third degree polynomial to approximate f

Q: Ex. 3. Find the Taylor polynomial of order 3 for the function f (x) = ln (3x – 2) at point 1. Use it…

A: As per guideline we have to solve only one

Q: (a) Find a Taylor polynomial of degree 4 for f(x) = sin(x) expanded about x0 = 0. (b) Find the error…

A: Here function f(x)=sin(x) , 4th order derivative at x=0 is 0, so degree of polynomial is of degree…

Q: In th given equation as follows , approximate the function at the given value of x, using the…

A: The value of a polynomial f(x) at a particular point x=a can be obtained by substituting a for x in…

Q: Q1) Find the Fourier series of the function: -1<x<0 f(x) = %3D 0 <x<1

A:

Q: t is the fourier series of f(x)=x^3+2 at (-L, L)

A: We have to find the fourier series of fx=x3+2 at -L,L

Q: Q.7 (a) Obtain the Fourier series of the function f(x) (b) Show that, fcdu=e¹.x > 0. = {1,05x5

A: Using the Fourier cosine integral representation for the result of (b)

Q: Find the Maclaurin’s polynomial of degree 3 for  ( a ) f ( x ) = (1 + x ) e 2 x ( b ) f (x) = ln(3…

A: Given, f(x)=1+xe2xf(x)=ln(3+ex) To find: Maclaurin's polynomial of degree 3

Q: a) Find the degree 3 Taylor polynomial T3 (2) for the function f(x) = 4 cos(r) centered at the point…

A: The function f(x)=4cos(x) centered at the point a=π4

Q: Find the second Taylor polynomial P2(x) for the function f(x) = x sin x about xo = 0 a. Find an…

A: Given function is: fx=xsinx

Q: 20. The function e* outgrows any polynomial faster as x→ oo than any polynomial Show that e grows…

A: Here we have to show that exponential function grows faster than any polynomial as x goes to…

Q: Q2. Find the Fourier series for the function f(x) = [x – x² for – n < x < a]

A:

Q: Find a Taylor polynomial of degree 5 for f(x) = 1/(1 – x) expanded about xo = 0. | Find the error…

A: Taylor Polynomial: The Taylor polynomial of the function fx of degree n at x=x0, is given by…

Q: [CLO2] Find Taylor Polynomial of degree N=3, P3(x), for f(x) ex expanded about xo = 0. 3 ek Lk! k=0…

A:

Q: - 1< x < 0 0 < x < 1' (e* 3. Find the Fourier series of f(x) = {". f(x) = f(x + 2).

A:

Q: 2. Find the Maclaurin polynomial of f (x) = cos x.

A: Using maclaurian series of polynomials,

Q: 2.r if 0 if rl<x

A:

Q: Q1: Find the Fourier coefficients and Fourier series of the triangle function f(x) defined by (E+ x,…

A:

Q: 3. Use the third degree Maclaurin polynomial of f to approximate th value of 0.2 ln(1.1), give your…

A: Macluarin polynomial of the function

Q: 2x 1- if 0<x<a/2 Find the Fourier series of f(x)= f(x+7)= f(x). if a/2<x < T

A: The given problem is to find the Fourier series expansion of the given periodic function with period…

Q: Question 2 Find the Taylor polynomial P5(x) centered at x = 0 for the function f(x) = 5x² – 3…

A:

Q: 2. Find the MacLaurin polynomial of degree 16 for the function F(x)= So sin (6xt²) dt.

A:

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

A:

Q: ) Find Fourier series of the periodic (T = 2T) function f(x) = x² ,- n < x < n

A:

Q: 14. Find the third order Taylor polynomial T3(x) of the given function at the given point. (a) S(1)…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: (12) The coefficients (a, ) of the Fourier series of the function f(x)= x;-7<x<a, is

A:

Q: F(x) JO sin(7t) dt.

A:

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

A: Given: To find the Fourier series of the function  is given as,

Q: Given the function below, find the 3rd degree Taylor polynomial T3(x) centered at x = 5. Que Que…

A:

Q: Question 2 Find the Taylor polynomial P4(x) centered at x = 0 for the function f(x) = 2x – 2 cos(x).…

A:

Q: a. Find the Taylor polynomial of 6th order at a=- 2 b. Find error at x = π. X c. Graph the original…

A: The given function is fx=cos2x. a. Find the Taylor polynomial of 6th order at a=π2. b. Find error at…

Q: Find T4(x): the Taylor polynomial of degree 4 of the function f(x) = arctan(11a) at a = 0. (You no

A:

Q: What is the value of (do) for Fourier Series of the function f(x) = x², - TS x < n? %3D 2n3 c) 3 d)…

A:

Q: Find the Taylor polynomial P4(x) centered at x = 0 for the function f(x) = x – 4 cos(x). a) 0-4-x+x*…

A:

Q: x² in the interval (-x, 7) 2 a) Find the Fourier series of f(x)%3D b) xe* Find the Fourier transform…

A: Since you have asked multiple questions, we are answering the first question for you as of now. If…

Q: Q1/ Find the Fourier series for the Function f(x) = 4 – X² ,When – 2 <X< 2

A:

Q: The polynomial of degree 3 P(x), has a root of multiplicity 2 at x=5, and a root of multiplicity 1…

A: Root Multiplicity is the multiplicity of a member of a multiset is the number of times it appears in…

Q: Q1/ Find the Fourier series for the Function f(x) = 4 – X² ,When – 2 < X< 2 %3D

A:

Q: Let g (x, y) ) = 11 sin(xy) — 13x² ln(y) + 20. Find the degree 2 polynomial, p, which best…

A: Given: The function is g(x,y)=11sin(xy)-13x2ln(y)+20 To find: The degree 2 polynomial which best…

Q: a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x² e-2t sinh t…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Q4: A. Find The Fourier series for the function defined by 2k * (x) if 0 <x <; f (x) = 2kx Tl-x) if…

A:

Q: 9. Write the Taylor polynomial of degree n for the following functions: a) S(x)=xe**, n= 8 b)…

A:

Q: Part a: Find the 7th degree Taylor polynomial for f(x) = x³ e2x centered at x = 0. Part b: Use your…

A:

Q: The 2nd degree polynomial that interpolates to f(x) = cosx + sinx at x = 0, x= π/2 and x = π is best…

A:

Q: [2] Find the Fourier series of the function f(x) = sin(4x) {ain(kx) -T≤ x < -π/2 -π/2<x< π/2 π/2 ≤ x…

A: Solution