Find the solution of the following problem: Uu = Uga I> 0, t>0, u(x, 0) = 2 u(0, t) = 0, t2 0. - z, u,(a, 0) z, r20, 2.

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: P= (2,3,4) Q =(4,6,8) Check my work: rlt) = [(4,6,8)-(2,3,4)].t 6667-₤14,6,8) (2,304) r(t) = r' (t):…

A: The given function is f(x,y,z)=z2, and the points are P(2,3,4), and Q(4,6,8). We need to check…

Q: For yx + 2x + cx = 9 ,m = 3,Find c at (3,1)

A: Given y2x+2x+cx=9 . m=1. We need to find c at (3,1).

Q: Find f, (x.y) and f, (x,y). Then, find f, (1,-3) and f,(-1,- 2). f(x,y) = - 5xy + 2y +6

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Q: The equations cos(u) + 10uy2 + e + 2 = 0 and 2ye" + 4x2v - 3xcos(z) +1 =0 are solved for u and v as…

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Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: The equations xcos(u) + luy? + e² + 2 = 0 and 8ye" + 4x?v – 3xcos(2) +1= 0 are solved for u and v as…

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Q: If X = /1 - t and y = t 3 - 2 t what is y'when t = -2? A - 20 /3 B none of the choices - 20 D - 28…

A: We have to find y'.

Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

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Q: +タ x2 – 1

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Q: Evaluate |(a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b₁ e²a+b; y = a² + t² + 1 да

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Q: Find the equation y = f(x) passing through the points (-11-21), (1,15), (2,12) and (3, 3)? Find also…

A: We will use the Lagrange interpolation method. We have: x x0=-1 x1=1 x2=2 x3=3 y y0=-21 y1=15…

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: 7. (D5 – 2D³ – 2D² – 3D – 2)y = 0 8. (2D3 – D² + 36D – 18)y = 0; when x = 0, y = 0, y' = 2, y" = 4

A: Note:- this is multiple questions and you have not mentioned is here which question you want to…

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: The function u(x, y) obeys, 8²u Ərəy = -2e

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Q: 7. Solve: dy x + 3y d.x 3x + Y

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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: 30. Which of the following is the value of f.(2, -1)? O -13 O 50 O 106

A: Given :              f(x, y) = 2x3 + 7x2y3 + 8y3 + 3x - 2y + 10   To find the value of fx(2,…

Q: Find ∂w/∂v, if w = 3x4-5y3+z5-10, x = 3u-4v, y=5u+2v, z = u+8v. Write in terms of the two…

A: Chain rule of derivatives

Q: 1 4. (1+2)y/ + 2ry = (1+2)y

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Q: 8. (2D3 – D² + 36D – 18)y = 0; when x = 0, y = 0, y' = 2, y" = 4 %3D %3D

A: Solution

Q: A company produces two types of solar panels per year:x thousand of type A and y thousand of type B.…

A: Given that,

Q: Q4\ If A(x,y, z) = 3x²i + 3zj – 3xk find the Div (Grad A). %3D |

A: Explanation of the answer is as follows

Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

A:

Q: It is the case that (x4 – y4)", where A=7 and n > 0 is a parameter, simplifies to x" – y". Please,…

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Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: -

A: Given function is: fx,y=2x3+7x2y3+8y3+3x-2y+10 We have to find fxx,y.

Q: y"- 5y + 4y ez.

A: Use second order ordinary differential equation rules

Q: The equations xcos(u) + luy² + e² + 2 = 0 and 9ye" + 4x²v – 3xcos(z) +1=0 are solved for u and v as…

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Q: 2 ( D° _ 2D - 20 - 3D - 2) y = 0 = 9

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Q: 2 2 ex: f(x, y, z) = x² - by ² fx (x, y, z) = fy(x, y, z) = fz(x, y, z) = 2 ezete

A: f(x, y, z) = (x2 - 6y2)/(y2 + 2z2)    => fx(x, y, z) = ∂/∂x [(x2 - 6y2)/(y2 + 2z2)]…

Q: 07. For the equation ginen below, evaluate y' (2,2) paict c५ +्2%-02 3 3r- + at the y at (2,2)=? %3D

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Q: Solve the P.D.E utt = 16 uxz2 s.t u(0,t)=u(5,t)=0 , u:(x,0) = 0, u(x,0)=x² (5 - x) ,h=1,k=0.4

A: See this solution in below

Q: '5. Solve the equation 3uy + Ury 0. (Hint: Let v = = uy.)

A: To solve the given equation  3uy+uxy=0 .