Region B: Computing the integral of the function f (x, y) = (x + y) cos (x + y), with a triangle consisting of vertices (0,0), (a, a) and (a, -a).

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

A:

Q: Write the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r…

A: f(z)=(r+r1​)cosθ+i(r−r1​)sinθ   Explanation:

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: b) Evaluate: i) Sx(V ++x) dx -2 10 dx ii) J1 x(10+Inx)³ jii) Jo 1+x? dx

A:

Q: Find the maximum value of  sinx+cosx at [0,pi]

A:

Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

A:

Q: Prove that dl = (Vu) x (Vv) - do.

A:

Q: (z)dz

A:

Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: X f(x) 0,0 0,5 1,0 2,119 1,0 15 20 2,910 3945 5,72 2,5 8,695

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Find the Jacobian of the transformation x = u - 3v, y = u² − 6v

A: Solution :-

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

A:

Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…

A:

Q: 8. Consider the complex function f(z) = x² + y² + 2ixy. a) Show that f'(31) does not exist. b) Show…

A:

Q: cos x + sin x - e¯y 2(cos x - cosh y) Determine the analytic function f (z) = u + iv, if u - v = and…

A:

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.