{ 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 f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: Find the laplace of  f(t) = cos(root2)t + sin (3t)

A:

Q: a2f дхду' a2f 2. (a) If f (x, y) = x tany + ye-2*, find and What do you notice? дхду (b) If f(x, y)…

A:

Q: The maximum directional derivative of the function f (x, y, z) = x'y°z° at the point (1, 1, 2) is a)…

A: Given problem:- Find the maximum directional derivative of the function f(x, y, z) = x³y³z³ at the…

Q: 6- Determine the domain of the function f(x, y) = In(x² + 2y² + 1) + arcsin Vx - 1 a) D = {(x, y)| 1…

A:

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

A:

Q: Cos X. is iF C3)?

A: Given,            Consider the function Fx whose second derivative is F''x=18x+3cosx.           Also…

Q: 3 z'= 2(x"+Z) Arrang e in linear form: dy Q) or dx

A:

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

A:

Q: Which functions form the basis of solutions for the ODE y – y" – y" +y' (x) = 0? O {1, e ?, e², æe }…

A:

Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

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

A:

Q: i) J₁(x) = e-ix €-15 (2)" , Fi(n + 1; 2n + 1; 2ix) n!

A: Aim: To prove the relationship between Bessel function and hypergeometric function,.Definition…

Q: Find the daigram only for the equation  z =x^2+y+cos(x^2)+siny

A: z=x2+y+cos(x2)+siny

Q: Find div F and curl F if F(x, y, z) = 9ei - 3 cos y j + 2 sin² z k. div F= curl F=

A:

Q: f(seca tan a – 8a")da tan a + a° + c sec a +a8 +e - sec * – a8 +c sec a – a° +e sec a +8

A:

Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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: Determine the set of all z where h(z)=cos(z)/e^z is analytic.

A: Analytic function A function fz is said to analytic in the region R if the derivative of fz exists…

Q: Now H= [² 2 id 2² H эрг = Ho 2² [Ho Sin (Kr_wt)] ar 2 [2 Ho Sin (Kr- wt) Ho 2/ [cos (kr-wt) x] K Ho…

A: They have derived the partial derivative. Our aim is to explain the derivative rule.

Q: y +2ry = e c) Find the general solution of the equation using the x^2y = u and transforms, e^x=v

A:

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: estigate whether the function u(x, y, z) = e^(3x+4y)cos(5z) is a harmonic function, where harmonic…

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

Q: 5. Find all analytic functions f such that Ref + Im f = ry.

A: We need to find the analytic functions f such that Re f+Im f=xy. Consider the function of the form…

Q: Draw a direction field for the equation y'=y+x-y^2 for -5 < x, y

A: The direction field is obtained as follows:

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.