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

Q: The linearization at a=0 to √2+5x is A+Bx. Compute A and B

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Q: Solve the pollowing: り ( 2+J(xtjy) X=? ye! (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)-2j x=?…

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Q: What is the order of y"(t) + 9y(t) = 10?

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Q: then fxy Q4: If f (x, y,z) = x²y³ – y²z3 %3D -

A: we have to find partial derivative

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

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Q: Undefined Slope 17,9), 17,2) X, - X m= 2-9 18 - 16 m%3D y - y = m (x-x)

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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: (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: Consider generalizing in the following way: N customers line up for their sandwiches, and you are…

A: The probability of an event is the chances of happening of the event. It can be defined as the ratio…

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: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: IN For r(t) = (2t, t2, 1-t), find T, N and B.

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Q: (D2-3D + 2)y=e5x, Find Y = Yc+ Yp O a. 1 *C₁² + €₂²¹ +2³² 12 O b. ³² C₂₁ ²² +₁₂=²+ = 12e-² -5x 12 O…

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

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Q: = Determine the end behavior of h(w): a. b. a. b. O JO Op - 4w³ - 3w4 w6 - 5w5. C. d.

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Q: 9) If y = 3x +x² - 5 and z = x2 - 12, find 2(y +z).

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Q: If √(x) + √(y) = 7 and y(36) = 1, find y′(36) y′(36) = ?

A: Taking derivative with respect to x,

Q: 1 (D² – 3D + 2)y 1+e¬x

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Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: Show that 1 1 1 a² y? 2 = (y? – x²)(z² – a²)(z² – y²) -

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Q: 3 - 9, y(0) 33 - 30 – 13 a(t) = y(t) = %3D

A: Given,       x'y'=53-30-13xy     x(0)=-9, y(0)=33

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…

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: Find a, b, c, d for P(x) : = ax3 + bx? + cx + d if P(1) = 11, b = 3d, a = 2c and P(x) = Q(x) + x+1'

A: Polynomial and remainder

Q: (D² - 3D + 2)y=e5x, Find Y = Yc + Yp a. 1 0² C²²² +₂²³ +2² Cet C 2 2x 5x 12 O b. O C. O d. Ce + Ce 2…

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Q: d²x is dy2 15 If x = (3 2y)5/2 , then 15 А. — A. -15(3 - 2y)1/2 В. 2 (3 2y)1/2 C. - (3 2y)1/2 D.…

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Q: Y = -2X, then p(X, Y) = 1?

A: Solution

Q: If f(x,y) = In(x?y² +3x) find- дудх O a. 12x?y (x²y² + 3x)? O b. 6x?y (x2у2 + 3x) Ob. 6x²y (x²y² +…

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Q: (8) If w = 5x² + 2y², x= -3s+t, and y = s – 4t. Find and Əw as

A: The objective is to find the partial derivatives .

Q: differentiate the following: Q(y)= y3/3 + 3/y3

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Q: If ZY = 2x + 9, ZM = 10, ZN = x + 3, and MW = x, then x = (A) 2 + V34 BD bisects LABC and D lies-on…

A: Given:

Q: Use the Laplace transform to solve the given system of differential equations. dx dy + 7x + dt 1 dt…

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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.