By using the Fourier transform, find a solution for the following problem (PJu,(1, x) = ux(!, x) + 3f², xe R, 1 > 0 u(0, x) = sin(x), xER

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: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: „T7/12 (1 + etan 3x) sec 2 3x dx Зе

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

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Q: Find f'(z) of f(z) = 3πi.

A: Compare the given function f(z) = 3πi. with f(z)=u(x,y)+i v(x,y) So,  u(x,y) =0 and v(x,y) = 3π

Q: For the linear operator L = D^2 −4D + 8, determine L(y) for y = e^(2t), y = e^(2t)sin(2t), and y =…

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Q: Let (t) = Find '(t) '(t)=<

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

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Q: Use the rule for square roots: f'(x) 2/ F(x) V F(x) to find the following derivatives (quickly d V…

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Q: Find / dy dx 174= √² y = √5 +1 and S=16x²= 2√

A: Note:-Since you asked multiple questions, according to our policy we can answer only first the…

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: Let f(1) = (1 + 2x + 2)*

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Q: Compute r"(t) and r'''(t) for the following function. r(t) = (7t2 + 4,t + 3,6)

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Q: nd r'(t), r"(t), and r'(t) · r"(t). r(t) = 4 cos(t)i + 3 sin(t)j a) r'(t) b) r"(t)

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Q: Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|1 ƒ (x) = = { 1 + 0 is ƒ…

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Q: Given the function g(x) = :/ V4 + sin(31) dt, 2x3 use the Fundamental Theorem of Calculus Part 1 to…

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Q: f(x, y) = e-7x sin(2x + 5y) of gl& дх af ду || 000 ---

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Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

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Q: Suppose that 4x² + 2y² = t² and y=tsin 0. Find ду (27) ət 0 and at ?x

A: The given equation is y=t sin θ. Consider sin θ is a constant term.

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 fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

Q: 50, dex(+) = -25 (+ + 2) + 25 (1-0) + 15 (t-1) at 2 = -√(x + 2) + 251f) + 5lt-2) By using…

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Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

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Q: What is dy/dt of the given? Show both the simplified and unsumplified answer.

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Q: ind the equation of the curve whose y" = ○ y=2 sin-¹ (2) — 4³-√3 -1 - O y = y = sin¯¹(x). X sin (x)…

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