Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

Q: i) Find the tangent and normal lines to the curve r*y° +sin(xy)+ln(1+y)+sin(2x) = sin(2) at the…

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Q: Perform one iteration of the Newton's method to minimize the function f(x1,x2) = 2(x2 – x?)² + (1 –…

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Q: use the laplace transform to solve the initial value problem y''- 4y'- 4y = t^3          y(0) = 1,…

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Q: 3. Use Müller's Method to determine all the roots of f(x) = x' -x² - x– 2 Choose x2=1.0, Xo=x2+dx2,…

A: Given:- fx=x3-x2-x-2 x2=1.0,x1=x2-δx2  ,x0=x2+δx2,  δ=0.01

Q: By the odd extension method applied to the function f (x) = e¯2x, wherex > 0, the Fourier integral…

A: Given the function  fx=e-2x

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: (d) Use Fourier Sine transform to solve: a'u du əx² ay² 00; [u(0,y)=0, u(x,0)=f(x); (u(x,y) →0, as…

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Q: Solve B. V. P Ut = kuxx, -∞ 0 u (x,0) = e¯|x| By using Fourier integral

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: Suppose f(x)=x^9(6−5x^7) a) The roots of f(x) are x b)As x→∞, f(x)→ c)As x→-∞, f(x)→

A: Given,           f(x) = x9(6 - 5x7)

Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: The slope field for y' = x - xy is given below. Sketch the solution that satisfies the condition…

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Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

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Q: y The function f(x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree 2x

A: Follow the procedure given below.

Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt >0

Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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Q: Use the Superposition Principle to solve the ODEy′′ − y = x^2 + sin x

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Q: f(x) = Cos (3x) as a 6th degree polynomial centered at x = 0. Hint use the following: P₂(x) = ƒ(0) +…

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Q: Show that the function f(x) = x’ + 1 is invertible from R to R.

A: First prove that the  function is one -one  let f(x)=fyx7+1=y7+1x7=y7x=y therefore, the function is…

Q: find the time taken by an igloo in the shape of a parabola y=5x^2 which is hitted up at the initial…

A: Solution: The Gauss divergence theorem states that the total flux of a vector field through a closed…

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: As per the question we are given the definition of Fourier transform of f(t) as F(ω) Amd from that…

Q: kx _f(x) = ek

A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…

Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

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Q: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…