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Q: Q5\ If z = x + jy, where x and y are real, find the values of x and y when 3z 3z + 4 %D 1- j 3- j

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Q: Given f(x, y) = æ® + 6xy³ – 2y², find fzz (x, y) = fzy (x, y)

A: To find fxx(x,y), take the partial derivative of f(x,y) with respect to x then again take the…

Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: -2xy 3) y' = iy = -5 when x = 2 Ans: exact; x²y + y = -25

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Q: O Find The desivative of the following xy = 8 O y = 2re" © Cos (xy) = 4x² - 3y? 3D8 %3D 2. %3D

A: (a) xy=8 (b) y=2xey (c) cosxy=4x2-3y2

Q: Find Sol. of +2Y +るY +6Y whe hイ

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: Q5) ẩ.ẩ jolve the eẩqẩuatẩionj; 2x²y dy/ldx + 2xy' +1= 0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: EX: EXPress i w X.+24+2 where. w and. w in termsfu.amal.V. Z24. o..... ...

A: Chain rule: If w is differentiable function of x, y, z and x, y, z are differentiable functions of…

Q: The substitution u = r changes the integral 2xe²° dæ into 2ue%² du Select one: O True O False

A: Given that:                       1. Substitution of u=x3 in ∫012xex2dx into ∫012ue9u2du2. k≠0, then…

Q: x' = 2x + 3y – z y' = x + z z'%3D 4х — 2у + 62

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Q: 2 x 9 = +9 dy %3D

A: As per our guidelines only one question can be solved. The solution is given below for the 1st…

Q: Evaluate for: x = -2, y = 4, and z = 16 * J16 - (y +x)? |-2| 6. -14 O 2 18

A: To solve the given expression with  x =- 2, y = 4 And z = 16

Q: Calculate fxxyz if flx, y, z) = 5x3 + 6 x?y3 + 2y3 + 2z³ . %3D OA. O A. Szzy: = 3x2 - 3y? - 3z? %3D…

A: We have to find the derivative of a function with respect to X Y and Z which we can find by…

Q: Solue each of Hhe following ystem l10 using to augmented mátrix Mi -N=3 x+3y 3x + 3y +4z =17 +4z=17

A: The system of linear equations is given by : x+2y-z=3x+3y+z=53x+3y+4z=17 We have to find the…

Q: 13. f(x, y) = x³ – y³ – 2xy + 6 %3D

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Q: -6 Let y = ( 5x + . Then dy - A(5x + )" (5 -)". = A 5x + where %3D B = C = D =

A: To find the derivative of y with respect to x

Q: (a)2t – 2 + (y')? + 2ty'y" = 0, y(1) = -÷, y'(1) = 1 %3D %3D

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Q: y dy Find using the substitution +5= √√y+2. √x+2 A²/(√y+2-5)(-5√/y+2+y+21) +C 3 ® ²/(√y+2-5)…

A: ∫ydyy+2 Substitute, u+5=y+2 Then , du=12y+2dy ⇒2y+2 du =dy ⇒2u+5 du =dy and y=u+52-2=u2+10u+23

Q: Let z=xin(x2+y2-e4)-176xy, x=te, y=est, If the value of z when s=2 and t=1 is equal to Ae?+Be4, then…

A: Explanation of the answer is as follows

Q: YQʻ +y² = x 1-2xy2 2y(x2+1) „y' :Select one True False

A: Differentiation

Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

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Q: Evaluate the iterated i 3 5. ('y dx dy xp 4x _JJ

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Q: Find curl (8z i + 9xj+4y k). curl(8z i + 9x j + 4y k) = ( i )i + ( i j+( i )k

A: topic- curl of a vector

Q: ii. (x + y)dA Where R = {(z, y)|1 < x² + y? < 4, x < 0}

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Q: Consider F = (5xyz, 5x² + 5y² + 3z², 8x + 4y + 3z). %3D Then curlF = (4+ Az, 5æy – 8, Bx – 5æz) What…

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Q: Find Duf at P. f(x, y) = 3(1 + xy) 2; P(5,3); u = 1 i+ NOTE: Enter the eract answer. Duf 62

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Q: Calculate yk) (0) for 0 <k < 5, where y = 3x + ax + bx? + cx + d (with a,b,c,d the constants) yO(0)…

A: Consider the given function: y=3x4+ax3+bx2+cx+d Hence, we can say that: y00=304+a03+b02+c0+d=d First…

Q: Evaluate the triple integral: A) 12 B) 24 C) 6 D) 18 3 2 (x+y+z)dydxdz

A: To evaluate the given triple integral.

Q: 2x+y y'3= 3+3 y2-x not exact. %3D Select one: O True O False

A:

Q: Let I = S (8x + 10y + 4+ 12xy) dA where R = [0, 1] × [1,2]. R Find I

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Q: ||xVx+2y dA, where R = y): 0sxs2, 2sys1-x use x = 2u, y=v-u R

A: Changing variable of integration from x,y to u,v and then integrating using beta function

Q: 2x Demuestre que y=c1ex + c2e* + c z e * + 3 es una solución de yll -2y|| - yl + 2y = 6…

A: Here, we need to justify that y=c1ex+c2e-x+c3e2x+3 is the solution of y'''-2y''-y'+2y=6. Now,…

Q: Perform convolution of h(t) and x(t) = (r(t) +r(-t)){u(t + 2) - ust - 2)1 %3D

A: Graph of x(t) is:

Q: • Which of the following is z when dz 3.r + 6y² + 4? a. 2 = 4x + 6y? + 4x b. 2 = a + 6xy? + 4.x c. 2…

A: Solution

Q: tind y 3 O y=(++ y =9tan 4 ® y= x (2x+1) (4) %3D 1-VX

A:

Q: Find curl (4zi + 5x j + 6yk). url(4zi + 5x j + 6y k) = (i )i + (i )j + ( i

A: Topic:- vector algebra

Q: Find the solutinof DiFfnential y y(0) = 1, 11) y-4y'+4y=U, (0), -3(0) 12) y+2y'+2y = 0, (0) 35

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Q: Evaluate: 3z dz when C: z = 0.5et (0 < 0 < T) %3D

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Q: = 3r and Express and ds interms of r and s, where w = x² + y?, x = r – s and y = r+s. dw 5r and as…

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Q: If f(x) = y (8 + h) – f(8)_ 4x2- 20x, simplify %3D O 44 + 4h O 44 8h O44 +9h 44 11h 44 3h

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Q: see attached for question

A: For two congruent triangles, their corresponding sides and angles must also be congruent. We can…

Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation

Q: 9. Calculate y' for y +2xy = 3x-2y %3D

A:

Q: 2. Given y = 25e-2x verify that y' + 4xy = 0 Your answer

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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.