{ S x, a| < 2, The Fourier integral of f (x) = is %3D 0, Ja| > 2, A) roo sin 2w-2w COs 2w sin rwdw w2 0o sin 2w-2 Cos 2w sin rwdw B) ° C)? 0 ∞ sin 2w+cos 2w sin rwdw w2 8. D) 2 0 sin 2w+2wcos 2w sin æwdw w E) w sin 2w-Cos 2w w2 sin rwdw

Q: 2πT 1 I₂ = So dt. 13 + 5 cost Let I be the unit circle {z e C : |Z| = 1} parametrised in the…

A: Solution:Let z=eιθThen z=cosθ+ιsinθ (By Euler's…

Q: Ou :? u =x +y +:, x=e" cos 21, y =e"21, : =e" = e" (cos 21-sin 4t +&t +8) +2e Ob. e (cos 21 - 2 sin…

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Q: find the curl of U = exy ax +sin(xy)ay + cos2(xz) az

A: U=exyax+sinxyay+cos2xzaz

Q: c) y = (x-2) 3 x² (x-1)(x+5)4 [Hint: use logarithmic differentiation]

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Q: 6. (a) Recall that sin z = ¹2; cos z = (i) Find real and imaginary parts of sin z and cos z, for z =…

A: Note : '' As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

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Q: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: Y 4 1.2) ["se sec ¹ √e de e 20) ff 2² 1 x² ln x dx

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Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (3e' cos t)…

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Q: What does is mean for two functions f(x) and g(x) to be orthogonal

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Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: { e, a| 1, The Fourier integral of f (x) = %3D A) roo w sin w-cOS w sin zwdw w2 roo sin w-CoS W sin…

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Q: sinx sinx +x The integral cosx - e +e -dr may be written as mensinx + pr+ gerx + C, where m, n, p,…

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Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: Find dy: dx 1) y = = = tan // -1/3 333 2 y = sec¹ 5x 3) y = cos cos2x 4) y = cot" ¹ 2 ² + tanı X/N…

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Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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Q: + Find the maximum value of isu = Sinn Siny Sincnty) U

A: The given problem is to find the maximum value of the given function u=sin(x)sin(y)sin(x+y).

Q: of the apples is equal to 3 of the oranges. If there are 12 mor 5 In a fruit stall, - - annles than…

A: Fraction:  A small part of something.  In other words, numerical value that is not a whole number A…

Q: Use implicit differentiation to find dy/dx. 18) y cos = 4x + 4y - y sin A)- cos B) sin 4y 4y2 D)-…

A: 18.we have y cos(1y) =4x+4y⇒dydx(cos(1y) )+ysin(1y)×1y2dydx…

Q: 2. y" +4y= sin2x + x2 using inverse operator method

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Q: -2x Use Green's Theorem to evaluate [(3 ye^²* − 7 sin² (3x³)) dx + (5x² + 2x²y² +8e³¹²-7x+²) +2) dy…

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Q: Question 8 Evaluate the Integral J sin³y cosy dy. A - sin4y +C B -sin3y +C - sin*y +C -sin³y+C D

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Q: F.(3e-3 sin(2x')) is equal to 2 3. n 4+@² 3 cos 8 4 3. 7(1+o² 4 cos 4 4 1 3, 1 +4cos 4. 4 2 1+@ 4…

A: Use the following formulas to calculate the Fourier cosine transform. Fee-ax=2πaa2+ω2…

Q: can you find C if x = 1/2 and y = (square root of 2)/2 thank you so so muchh!!

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Q: In (secx) a) | sec2t dt + cot x

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Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

A: