Suppose that W (y1, Y2) (t) = 4, and y3 Yı – 3y2. What is W (y1, Y3) (t)?

Q: if y = x+ v3+ 2x then prove that (3+2x2) + 2x 2y = 0 %3D dr

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Q: 1 (g) √ F+x(a+b)+abdx

A: To evaluate the following integral.

Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

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Q: if y = 3x² – 4r³ + 3ª + VI + a, then dy/dr is:

A: Given that     y = 3x2-4x5+3x+√x+π Here we have to find dy/dx . We know that        dxn/dx = nxn-1…

Q: (5) If z = xf (2) +g (2), then the value of Z. + 2xy- + y?. is Əxdy (а) -1 (b) 0 (c) 2 (d) 3г

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Q: (x-2)² + (y+1)² =16, find- A. 16 (y+1)³ d²y dx² B. 16 (y +1)³ C. 16 y³ D. 16(x-2)² (y+1)³

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Q: If f(x,y)=x³y +7xky2, find fx(1, -2) where k = 3

A: Given query is to find indicated partial derivative.

Q: Give an example of C = diag(c1, C2, C3) and D = diag(dı, d2, d3) where Tr(C) det(D), but C is not…

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Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: f(x, y) = 8x3 6x2y3 + 7y4 -

A: Given data:     The given function is: f(x,y)=8x3-6x2y3+7y4.   The expression for the partial…

Q: Differentiate in two ways: y = (x + ¹)(x - ² + 1)

A: We know that the product rules of the derivative d/dx(uv)=u*(dv)/(dx)+v*(du)/(dx)

Q: 3.2 X(x²-1)-y=xy* ;y(2)=-

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Q: Given f(x, y) = 2x³ – 3xy – y³, find fxx(x, y) = fay(x, y) =

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Q: 6xy — 2x — 8zx2 = 0 6xy — у — 2zy2 = 0 4x² + y² − 2 = 0

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Q: 3. Show that f(x, y, z) fxx + fyy+fzz = 0. = 1 x² + y² + z² satisfies the equation

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Q: (х? + 2у — 10у3х) if z у? (у? + 4х + 5у) dz -, find || дх

A: Given:

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

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Q: e) Solve [(-x'y)² + (x²y)³]²

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Q: Find Cyy(x.y) if C(x.y) = 9x² + 5xy – 2y²+4x-4y-8. Cy (x.y) =D

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Q: Let f(x, y) = x² + y² - 4 2 y-2 Find fay(x, y).

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Q: Let U(z, y) (2x +3)(y+5). %3D Select the correct expressions for Uz and Uy: (A). Uz= 2x+3. %3D (B).…

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Q: Iff (x, y) = 4x³ +7y², findf (1,2).f; (1,2).f, (1, 2). f (1, 2) = fx (1, 2) = fy (1, 2) =

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Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: I. If f(x, y) = x² – y² + 4xy – 7x + 10, find (a) f(2, 1) (c) f(x + h, y) (b) f(-3, 5) (d) f(x, y +…

A: topic - functions note : As per bartleby guidelines, we are supposed to answer only first three…

Q: . Let f(x) = x² + x + 3, g(x) = 5x + 3 and h(x) = 2x² – 4x + 1. Find the following: d. (fo h)(-5y)…

A: Composition of the function

Q: Given y = f(x), if f(2)= -3 f(4) = 5 f-¹(-7)=2 Decide if f(x) is invertible. Give a clear…

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Q: Find (f – 9)(y) if f(y) = 5y² – 2y + 1 and g(y) = -3y? – y –2. O (f – 9)(y) = 8y² – y + 3 O (f –…

A: Given 2 functions : f(y)=5y2-2y+1g(y)=-3y2-y-2 We need to find f-gy. Let's begin.

Q: For two points (x1, y1) and  (x2, y2) such that xi > 0, yi > 0 for i = 1, 2, we say  (x2,…

A: There are about 4 functions provided.To show:They are Schur convex or not.Concept used:i) Any…

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.