solve for the Fourier series f(x)=x^2 in (-1,1)

Q: find integral of sin-4x

A: Given: -

Q: Calculate the value of the function f(x) = sinx cosx at  x= 0.1 using the 4th order derivative…

A: Suppose fx is n times differentiable function then nth degree Taylor approximation for fx near 0 as…

Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: sin 0 -do 4+cos 0 Evaluate

A: Since 4+cosθ is never zero in 0 to 2π as -1≤cosθ≤1. So, 3≤4+cosθ≤5 So, sinθ4+cosθ is analytic in 0…

Q: QI/Use the Biseetion Method to approximate one of the roots of f(x) 3x 2x+ 6x-8 with interval (1, 2)…

A: We can solve this using bisection method

Q: Verify the power rule for integration n+1

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Q: 4. Determine exact values of 0 if 0 < 0s 2n given that tano - V3. Explain your process.

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Q: How are the derivative and the integral of a series of powers defined?

A: Consider the following power series with a radius of convergence R &gt; 0. Let

Q: The normal line to the curve y = -2x2 at a point in the fourth quadrant passes through the point…

A:

Q: What is Properties of fourier transform

A: Properties are:-  1.Linearity 2. Time shifting  3. Congugation 4. Area under x(t) 5.Area under x(jw)…

Q: Prove 9 coshx – 5 sinhx = 15

A: This is hyperbolic function equation so we want to find x value by thi equation so. firstly, we…

Q: tion of all components of v(3) correct to two decimal places.

A:

Q: Integral of √1-sin2x/2

A: Integral: -The function F(x)is referred to as the anti-derivative or integral of the supplied…

Q: Find Fourier sine transform of - and deduce that

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Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: 10. Determine whether | sin(x)dr converges or diverges. If this improper integral converges,…

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Q: Find the indefinite integral and check the result by differentiation

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Determine if the integral * 1+sin² # dx is convergent or divergent.

A: We can determine if the integral ∫1∞1+sin2xxdx is convergent or divergent using comparison test.…

Q: f(x) = cos(T.x)+ sin(27x).

A:

Q: 9 coshx - 5 sinhx = 15

A: Note the following result : cosh x=ex+e-x2  sinh x=ex-e-x2 . In above formula , x∈ℝ . To solve the…

Q: Find the indefinite integral and check the result by differentiation. dt F--3-3)- 8. 12

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Q: What is the integrable form of sin-cos- sin0 do?

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: logtan nx(2+ 4 cos nx) 2

A:

Q: 000 Find the solution of heat equation by Fourier sine/cosine transform, if initial temperature is…

A: Here we use separation of variables. Means we assume that  ......(i)  be a solution of the given…

Q: (2x³ + 5x-4) dx

A: Solved below.

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Assuming an initial bracket of (-0.5, 0), what is the approximate value of the root of f(x) = 3x +…

A: The false position method can be used to calculate the root of the function. The formula for the…

Q: Give 5 example of Reciprocal rule of Basic Integration Formula.

A: Given: Give examples of the reciprocal rule of the basic integration formula The reciprocal rule for…

Q: Differentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between…

A: Maclaurin polynomial of degree 4 is P4x=f0+f'0x+f''02!x2+f'''03!x3+f404!x4.

Q: Express the definite integral as an infinite series. 7e dr

A:

Q: find the fourier series for the half-Period sine of the function fx) = sinx inthe period 8. xx Then…

A: Given that, f(x)=sinx in the period 0&lt;x&lt;π. ∫n=1∞1(2n-1)2(2n-1)2. The objective is to evaluate…

Q: Use Newton's method to estimate the solution to sin(theta) = 1- theta/2 up to four iterations.

A: Given function is: f(θ)=sinθ+θ2-1 Rewriting function in other variable: f(x)=sin x+x2-1 Newton…

Q: 2. Solve 3shn-sinx-2= over the interval [0,27). 2 sın'x-sinx-|:0

A: The objective is to solve the above expression.

Q: Compute the derivative of Sin x in two ways: (i) Using the chain rule. (ii) Taking the derivative of…

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Q: Compute the fourth derivative of cos(x+1) - ln(x²+4) + x²²+1 with respect to x. Also, compute the…

A: Sol:- First part:- Fourth Derivative of given function:-…

Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: find the fourier series for the half-Periof sine of the function fxj = sinx inthe period x Then find…

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Q: Solve the integral| 7. tanz x sec4 x dx

A: Let I=∫tan52 x sec4 x dx. First, rewrite this integral as the following. Use the identity…

Q: Four positive numbers, each less than 130, are rounded to the first decimal place and then…

A: Let p,q,r,s be the four positive numbers and their product be w

Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: fer) sen ax %3D

A:

Q: Four positive numbers, each less than 80, are rounded to the first decimal place and then multiplied…

A: Solve the given problem.

Q: After separation of variables, if the constant is a negative value, how is the Fourier series…

A: Given  the one dimensional heat equation with some boundary conditions, i.e  ∂u∂t=k∂2u∂x2…

Q: This is exercise 26 of Section 7.5 page 460. Find the integral æ* sin(æ²) dx-

A: Answer is given in the picture

Q: compute the integral of    "(sinx * tanhx ) / ln(x+0.01)" from 1 to 5 to at least 6 significant…

A: Given :  ∫15sinxtanhxlog(x+0.01)dx

Q: What is the integrable form of sin-cos-sin0 do 2 2

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Q: Solve: the integrand (pi/3 sin5x) dx on the integral pi/2 to 3pi/2

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Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

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Q: 0 < x < 4 Graph and expand f (x) = 18 – x 4 < x < 8 period 8 in Fourier sine ser %3D

A: