use the inner product < p,q >= p(x)q(x)dx. to find the projection of p(x) q(x) = 5x + 2. = S'; x3 onto

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

A:

Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: Find ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.

A: Given that, fx, y, z=1-2xy2z+x2y           ...(1)

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

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: ху lim (x,y)→(0,0) Vx²2+y2 Get the value of

A: This is the problem based on multivariate calculus. To find the limit , we can convert given…

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

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: Find all residues of the function z (2-2) not including the residue at infinity. "

A:

Q: (2, -4); slope = -3

A: Topic = Coordinate geometry

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: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Find fxxyzz for f(x, y, z) = z°y2in x. fxxyzz = -12z?y/x2 O fxxyzz = -12zylx fxxyzz = -12zylx2…

A:

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: Find the image of the line z =3 +iy under f(z) = e

A:

Q: r(2,4) Sa (2y+x) dx +(3x– y)dy} along the straight line x-2t and Evaluate J(0,3) y=P+3.

A:

Q: Find the linearization L(x, y) of the function f(x, y) = (x^3)(y^6) at the point (-2, -2).

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.