Find the first three terms of the expansion, in ascending powers of x, of (1 – 2x)². Hence, find the coefficient of x² in the expansion of (1 + 3x)(1 – 2x)'². (i) (ii)

Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: Given: f(x)=ln3-2x,a=1

Q: Find the coefficient of x* in the power series 3x² +2x expansion of (x +2)(x-3) |

A:

Q: ] Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: The general formula for the derivatives is  dxndx=nxn-1 A taylor series is given by…

Q: Find the Fourier series expansion for: x2 f(x) = x + ,-n <x < n 4

A: Let us consider the function f(x) on the interval [-L,L] is obtained as…

Q: The coefficient of x^3 in the Taylor series for f(x)=ln(x) centered about x=1 is

A: Given function is f(x)=ln(x)

Q: The periodic function f (x) of period 2n is given by -n < x < 0 f(x) 0 < x < T a) Sketch the graph…

A:

Q: 4. Use the fact that the Taylor series for g(x) = sin(x²) is x6 x14 - - 3! 5! 7! to find g"(0),…

A: The function g(x) is given as  g(x)=sin(x2) Taylor series for g(x)=x2-x63!+x105!-x147!-------

Q: Find the Taylor series generated by f at x = a. f(x) = 3x* + 4x² + 2, a = - 2 The Taylor series…

A: Taylor's series of the function f(x) about x = a, is given by:…

Q: 5- Find the fourier series of function below: - n< x < -n/2 - T/2 < x < 0 0 <x < n/2 1/2 < x < n -2…

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Q: 9) Suppose the Taylor series for f(x) is f(x) = 1 – 2x + 5x² – 8x³ + 14xª + ..... What are the first…

A:

Q: Sin(x) can be expressed by Taylor series as below o (-1)"x2n+1 x3 = x x5 x7 sin(x) = En=0 (2n+1)! 3!…

A: IST METHOD SINx using fortan integer n real term , sum , deg write(*,*) 'Enter Degree'…

Q: Find the Fourier series representation of the odd extension of the function. Then, find the value of…

A: Fourier series for the odd extension of a function defined in (0,L) is given by fx=∑n=1∞ bn…

Q: 5. Determine the Fourier cosine series of f(x) = n² – x² 0<x<n

A:

Q: Find the first three non-zero terms of the Taylor expansion for the given function and given value…

A: The Taylor series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+..... Where, center at x=a.   Given:…

Q: Find the Taylor series for f(x)= 7x^2 - 4x  + 3 in powers of (x-1) where a = 1

A: Taylor series expansion

Q: Find the Fourier series expansion for the function s(x)=\+(10-x) for (-75xSa)

A: By using the formulas of Fourier series we solve the given problem as follows :

Q: he first four terms in the Maclaurin series expansion for f(x) = ln( (1+2x) / (1+3x) )  are

A:

Q: 4. Find the Fourier Cosine Series for f(x) = x – x² on [0, 1].

A: Concept Used: ( The Fourier cosine series) The Fourier cosine series is  fx=a02+∑n=1∞ancosnx where,…

Q: the function f(x)=xln(x-1) has a taylor series expansion at x=1

A: The Taylor series expansion of a function f(z) about z=a is given by the equation;…

Q: Find the Taylor series generated by f at x = a. f(x) = 2x4 + x2 + 4, a = - 1 The Taylor series…

A: Given, fx=2x4+x2+4 and a=-1 Taylor's series of fx about x=a is given by,…

Q: Find the coefficient of x* in the power series 4 3x² +2x expansion of x² +2)(x-3)

A:

Q: Find the Taylor series generated by f at x = a. 3 f(x) = x° - 2x + 7, a = 2 The Taylor series…

A:

Q: Find the first three nonzero terms of the Taylor expansion for the given function and given value of…

A: The given function is 3tanx, a=7pi/4.

Q: 1. Find the Fourier series of the function S -x if -4 <x<0 (x) (x + 8) = f(x) if 0 <x<4

A:

Q: b. Find the first three terms of the Taylor series expansion of tan x in ascending powers of( x -).

A: Binomial approximation and Taylor series expansion

Q: 8. Find the first two non-zero terms of the Taylor expansion for function f(x)=sin x and a given…

A: Let's solve.

Q: Find the n-th Taylor polynomials for f(x) = 1/x  about x = −1 and express it in sigma notation.

A: Given; f(x) = 1/x about x = −1 .

Q: Find the fourier series expansion in the f(x)=2x+1_range of the [-1,1

A: Given a function fx=2x+1 with range of -1, 1.

Q: Find the coefficient of x° in the power series 3. expansion of 2 x+2

A: Use expansion of (1+x)^-n to find the coefficient of x^6 .

Q: 1. Find the Fourier series for f(x) = x*. Find a bound for the error made in replacing x* by the…

A: F(x)=x4Let us consider ,x∈-n,nStarting with fourier sine series of sawtooth wave,x=∑n≥12-1n+1 sin…

Q: 5. Determine the Fourier cosine series of f(x) = n²– x² 0<x<1

A: We have ,  f(x) = π2 - x2 We need to find Fourier Cosine series of f(x). We know that , Fourier…

Q: Find the series of representation for f(x)=ln(14-x)

A: See the details solution in below

Q: (a) Find the Fourier series expansion of f(x) = , in -xSxSn. Hence deduce that 12 12

A: We will find out the required value .

Q: (8) Find the Taylor series for the function g(x) = 1/(x+3)2 at a = -2. Show your work.

A:

Q: Find the Taylor series generated by f at x= a. f(x) = x* + 3x +3, a = - 1 The Taylor series…

A: Taylor series is given by fx=∑k=0∞fkak!x−ak Compute the derivatives:…

Q: (a) Find the Taylor series of cos 3x at x = 0. (b) Use the trigonometric identity cos'x = }(cos 3x +…

A: To Find: i. taylor series of cos3x at x=0.ii. use trignometric identitycos3x=14cos3x+3cosxto find…

Q: In the Taylor series for the function 3x^2 − 7 + cos x expanded in powers of x, what is the…

A: Given:

Q: To evaluate the exact value of f(x) = (4x° + 7x - 9)(x29 - 3)29), what order of the Taylor series…

A:

Q: Find the first four nonzero terms of the Maclaurin expansion of the given function by using the…

A: Given problem:- Find the first four nonzero terms of the Maclaurin expansion of the given function…

Q: Find the complex form of Fourier series for e-x in -1<x <1

A: See the attachment

Q: 5) a) Construct a Fourier Series for f(x) = (x2 12x)for 12 < x < 3n - b) Briefly explain the…

A: To give the Fourier series for  f(x)=x2 -12x for x∈0,3π We are considering this range since the x…

Q: The coefficient of (x - 1)3 in the Taylor series for f(x) = In(x) centered about x = 1 is 4 -2

A: We need to find the coefficient of (x-1)3 in the Taylor Series expansion of f(x)=ln(x) about x=1.…

Q: f(x)=1/(3x+1), a=3

A:

Q: Find the Fourier series expansion of the function. - n < x < 0 f(x) = 0 < x < I

A:

Q: Find the binomial expansion of √(x² +1-y²) up to the fifth term.

A: As per the question we are given a bivariate function in variables x, y and we have to find its…

Q: Q3; Find the Fourier series expansion of a Triangle function for (-x5xSx). (25 mark)

A: We will find the fourier series expansion of a triangle function for ( -Pi ≤ x ≤ Pi )

Q: 8. Find the first two non-zero terms of the Taylor expansion for function f(x)=sin x and a given…

A:

Q: 3. Find the Fourier series of, - n<x<-1/2 f(x) = }0 - 1/2 <x <n/2 1/2 < x <n 1

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Q: sin(2x³) x² 11. Approximate justify your result. within 0.0001 if x = 1/3 using its Mac expansion…

A: Solution: Given function is, f(x)=sin2x3x2 sin(x)=∑n=0∞-1nx2n+12n+1! f(x)=∑n=0∞-1n2x32n+12n+1! x2…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.