2x + y 5z - 4y Find the total ditferential. W = 5z + 8x 10x + 5y 2 -x+ 5z – 4y dw = (5z – 4y)2" (5z – 4y)2

Q: f(x, y, z) = 3x - 2y + z- 12 = 0 g(x, y,z) = 4x + 2y - 25 = 0 h(x,y, z) = x- y²z-7= 0

A: Use the following formulae, to find the approximate solution of the non-linear system by the Newton…

Q: Find curl (6z i + 7x j+ 9y k). curl(6z i + 7x j + 9y k) = ( i )i + ( i )j + ( )k

A: Explanation of the answer is as follows

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

A:

Q: z" + 6z' + 8z = e – 6u(t – 3); z(0) = 2, z'(0) = - 6 %3D

A: Laplace transforms

Q: Find curl (6z i + 7x j + 8y k). curl(6z i + 7x j + 8y k) = ( i )i + ( i )j + ( i )k

A:

Q: Use chain Rule to find for 2. y = . +x²+x+1 I.W | 3. y = estn 3x Н.W

A: We have to find dydx using chain rule for the given function: 2.  y=1x3+x2+x+13.  y=esin 3x We know…

Q: Find (2) and (7) at the point (w, x, y, z) = (48,1, -2,-2) if w=3x²y² + 3yz - 3z³ and x² + y² + z² =…

A:

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming 1+z² Ⓒ √ 1 + 2/²/d= (A) -dz…

A: First of all, note that sec x=tan2x2+11-tan2x2⇒sec x+1=tan2x2+11-tan2x2+1⇒sec…

Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=< 3x2y-z, xz3+y4, -2x3z2 > To Find , grad divV  Let  V=< V1 ,V2 ,V3 > On…

Q: f(x,y,z) = xy + yz + zx, (2, - 2, - 1), A = 3i + 2j - 6k

A:

Q: X2 , 1 avuu. 3 VA 3. x = y3, 0 sy s1 about y-axis.

A: Given function is x=y^3

Q: * Minimize C=5x-6y Subject To 60–8xy. a. Find x*, y*, 2*, C* b. Use bordered hessian to verify.

A: This is a problem of optimization.

Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

Q: z+2 dz cot (z²+4z-3)

A: To evaluate: I=∫z+2cot(z2+4z-3)dz⇒z=12∫2z+4cot(z2+4z-3)dz...(1)

Q: y" + 4y' + 3y = U (t – n)e-2(t-r), y(0) = 0, y'(0) = 0. %3D

A: Consider the provided question,

Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: (D^3 - 2D^2 + D) y= xe^x + 1, y(0) = y'(0) = 0, y''(0) = 1. By inspection method.

A: We are given a third order non-homogeneous linear ordinary differential equation as : y''' - 2y'' +…

Q: x = 2 - t, y = 1 + t, z = 3t; x - y + 2z = (x, y, z) =

A:

Q: 2. y" – 2y' – 3y = e²", y(0) = 1, y (0) = 0, Yp(t) = -e2' /3 %3D

A:

Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

A:

Q: Calculate fw(-1, 2, 0, – 1) where f(x, y, z, w) = xy²z – xu? – e2²-y²–2²+2w=

A: Given that fx,y,z,w=xy2z−xw2−e2x2−y2−z2+2w2 To calculate: fw−1,2,0,−1

Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

A:

Q: Find: 군x, 군y, Zxx , 군ys, 군xy, 2sx = X+y Xy-1 Z =

A:

Q: Solve by Chain Rule 8 poir f(y) = /2y + (3y+ 4y²)³ %3D

A: Here clearly not mentioned, what to do with this question, but as we know chain rule is applied to…

Q: f(x, y, z) = z°y?lna fazyzz =? IIY -2z2 O A. 12y2z2 В. 2x2 -12yz O C. x2 y24 O D. x4

A: Partial derivatives

Q: Find the function y(x) satisfying -8/9 = 6x dx and y(-1) = - 4. dy :-8/9 The function y(x)…

A: Integrate the equation dydx=6x-8/9 with respect to x.…

Q: 3x + y + z = -2x - y x + 3y - Sz - 11 -7 A. (2, 3, t) В. (2, 3, 0) OC. (2 +t, 3 - 2t, t D. (2 - t, 3…

A: A general system of m linear equations with n unknowns can be written as {\displaystyle…

Q: b. y"-3y" + 4y = 0, y = 1, y'= -8, y"= -4 when x = 0 %3D c. y"+y"-0, y(0) = 2, y(0) = 1, y"(0) = -1…

A:

Q: y'+2y/x=x, y(1)=2, y(2) using h=0.1

A: given :y'+2yx=xy(1)=2, y(2) using h=0.1

Q: f(2ecz tan z - 6z")dz=_ • tan z+z+e secz+z+e • secz-z+e - secz-z+c •- secz+z+e

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 2. 5x + 3y > 15 7x + 2y < 21 x2 0 y 37 • Submit your activi File name: FINAL Example: FINALS

A: To plot the graph we first convert the given inequalities into E qualities . therefore  5x+3y=15…

Q: Lion 1-y If x = Show that 1+y dy V1-y

A:

Q: 26 + 4z4 – 2z2 +1 dz (z – 2i)6

A:

Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

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Q: Мaximize p = 10x + 10y + 15z subject to + z s 12 X y - 2x 2y + z 2 14 -y + z 2 4 x 2 0, y 2 0, z 2…

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Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given

Q: y(2x- xy ty')da-x (2x-y) dy =0, when x(4):0 %3D

A: Given: y(2x² - xy + y²)dx - x²(2x - y)dy = 0, when x(1/2) = 0

Q: roblem. y" – 2y' + 2y = e-; y(0) = 0, y'(0) = 4 %3D

A:

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: exy2z 1. Given Vx²y + y²z+10=0. Find 2. yz

A: Explanation of the answer is as follows

Q: - find x, y z Select one: а. X-3,у-2,z-1 b. x=3,y=-2,z=1 С. X-3,y-2,z-1 d. x=3,y=2,z=-1

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Q: Sove the IVP y" + 2y' + y : if 0 4

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Q: 5. y" + 3y" – 4y = 40t²H(t-2); y(0) = 0, y'(0) = 0, y"(0) = 0, y''(0) = 0 %3D

A:

Q: Given: Right AXYZ with XZ = YZ and XY 10V2 Find: XZ and YZ

A: Consider the right triangle XYZ,  XZ≅YZXY=102

Q: (a) The function z depends on u and v so that z = 2v(4- 3u)? u = 2x + 3y and v= 3x-2y az when x 0…

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Q: T(x,y) = x + xy + y - 12x + 2 on the rectangular plate 0sx<9, -5<ys0

A: We have to find absolute minima and maxima of given function.

Q: Find 2 by using the Chain Rule with y as a composite of dx y = csc(u), u = x3 + 2. %3D

A: Given: y=csc( u) , u=x3+2  To find dydx

Q: 2. f(x, y, z) = exyz² Find fxyz

A: