{ e, a| < 1, is 0, læ| > 1, The Fourier integral of f (x) = %3D A) roo w sin w-cOS w sin zwdw w2 roo sin w-CoS W sin rwdw B) Jo C) 2 sin w+COS w sin rwdw w2 D) roo sin w+w COS w sin rwdw roo sin w-w COS w sin rwdw 20

Q: Let ŕ ). ) - (0**) k (4 Sin 2+) + (4 cos 2 t, be the Position oF Perticle space in at time. Finc the…

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Q: Verify that the conclusion of the Clairaut's Theorem holds a) z = sin(xy) b) z = sin(x - y) c) z =…

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Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: Let F = cos(4t) i + 3tj+ 4t°k and G = t cos(4t) i + t j+4e#k Find the cross product F x G =

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Q: Question 1 Choose the correct statement(s) for the ODE d'y dx² dy dx A It is a 2nd order ODE because…

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Q: D2-2D- 3)y = 2sin x; y a. y = C,e™* + Cze* - cosx -sinx %3D COSX b. y = C;e¯* + Cze³* + =cosx – sinx…

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Q: of Then x y

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Q: əz Use Chain Rule to determine and where

A: We have to use chain rule step by step.

Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: se-2s -)=D 's²+45+3

A: Given,

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

A:

Q: dy dalam dr Gunakanlah diferensiasi parsial untuk menentukan pernyataan untuk kasus-kasus berikut:…

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

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=&lt;t sin t+cos t,2t2,sin t -t cos y&gt; Then vector is given by r→t=t sin t+cos…

Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: g) The integral S tan(vx) dx x cos2 (Vx)

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: SORU 7) S*-[(sint)i + (1+ cos t)i + (sec? t)k] dt =?

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Q: Consider two oscillating quantities: H1(r,t) = Re (Ae(2r+kz-« H2(r,t) = Re (2Ae“=/3+ke-us)…

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Q: Suppose that f'is continubus, f(o)-o and f(5)= e So f'(x) sin?Cf(x) dx 4) Calculate

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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…

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Q: Parameterize the following 1.) cos(z^4)+1y=1 (a surface) 2.) x^2 +5y^2=25 (a curve in R2) 3.)…

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Q: The antiderivative of the function sin (Gx+7) is:

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A: To find the derivative of  f(x)=arctan(ex) at x=-1

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A: ux,y,z=e3x+4ycos5z

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: 5) f(x.y)= *+y

A: We are solving the first question and for the next question post the question again andalso mention…

Q: prove that | Sinsy | dy лу ∞

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.