2. Solve the following Cauchy problem: u = u -0 0, u(x, 0) = 1 -1, u(1,0) = 4r, -00

Q: If (x, y)= x²y+e* , find; d. y е. b. $, с. Ф Q.4 (1)

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Q: (12) If y = a X"-b X*+1+5 is a polynomial and a » bER , then may by represent dX" by one of the…

A: n order derivative

Q: Show that Y parameter 8. (X₁+2X₂ +3X3) is not a sufficient estimator of the Bernoulli

A: Y=1/6(X1+2X2+3X3) is not sufficient estimator of the Bernoulli parameter

Q: Question 2 max Z= 3x,+2x, s/t X,+ x, 2 5 X, X, 2 4 with x,, x, 20

A: The given problem is to solve the given linear programming problem, we can use graphical method to…

Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: 8. х2 - ху -ах + ay

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Q: 5) U₂ = 5 Uxx t U(0,€) = 2 U(3,4)=-1 U(x,0) = -x

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Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

A: Here is how the set S is defined: S = {(a, b, c) | a, b, c ∈ [100], a &lt; b, a &lt; c}   We must…

Q: 23) -4V192X 25) -4V216xy'z

A: Given query is to simplify the expression.

Q: 4. If g(t) = et +e-i' then g'(t) is which of the following? 2et + 4e2t (A) e2t + 2+ e=2t 2et + 4e2t…

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Q: If x + y +z = 12 & x² + y? + z? = 96 & !+!+!= 36 then value ху Z of x + y³ + z³ is

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Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where x s player i's…

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Q: What are the coordinates of C' after its preimage, C(5,-3), is reflected over the x-axis? O (5,3) O…

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Q: Ay A'y A'y X y 1-1 -1 -2 2 1 3 -1 3 is given by x² – 4x +2 x2 O x? +2 x2 + 4x +2 4,

A: See the attachment

Q: Calculate the minimum value of 9x + 6y subject to the following contraints: x + y > 22 x + 2y > 27…

A: we solve this LLP by  graphical methods.

Q: Condition JW=3.6, j0=0.4

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Q: If s = (x² + 1)²/3 (3y² + 8y +4) 4(3z+2) 5, find d²s d²s dy² d²s dz²

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Q: 2. Jr.,(x) + Jvo, (x) = 2Y Jv (x) Ju (X) I need two examples to prove this property using the same…

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Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: 8. Solve the following IBVP: Utet = U +1, 0 0, u(0, t) = u(1, t) = 1, t20, %3D %3D u(r, 0) u(x,0) =…

A: Given problem is, utt=uxx+1 ; 0&lt;x&lt;2; t&gt;0u0,t=u2,t=1ux,0=-x22; ut=x,0=1; 0≤x≤2.......1 Let…

Q: 2x (x-6) 3.) y = (x-3)3 required:a) yand y"

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Q: Solve the following IBVP: Utt = 4uzz 0 0, u, (0, t) = u,(27, t) = 0, t>0, u(x,0) = 0, 0<I< 2n, T.…

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Q: 2 Sketch the level curve of the function f(x, y) = y - x² for c = -2,0,2.

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Q: Problem 1 (i) Si(1,72, 3) =+923+2r3-62172- 4r173 (i) fa(z1,z3,프s) -(2z +3rg + 4z3)2 (iii) fa(r1,#2,…

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Q: := rye" find z²y}e" (ry +1) O None of these Option 3 rye"" (ry + 2) ry²e# (xy + 2) Option 2 Option 1

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Q: 2. x = 2t + 3 and y = t – 4 for 0 <t< 4 (x,y) X y Domain:

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Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where is player i's…

A: The utility to player 1 is given as: u=xx+n1yAnw-x-n-1y;w&gt;0,A&gt;1 Also, Ak=Aw-x*

Q: In the xy-plane, the line tangent to the graph of 2 x² + xy + y² = 3 at the point (1, 1) has a slope…

A: Given equation is  x2+xy+y2=3  we need to find slope of the graph at (1,1)

Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: 10. Compute dy and Ay for y = x5 - 2x³ + 3x as x changes from 0 to 1

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Q: Solve the following Cauchy problem: 2px + qy-u = 0, u(x, 1) =

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Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

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Q: 3. (x4y4+x²y² + xy)ydx + (x4y4 - x²v² + xy)x dy = 0

A: The given differential equation is;  (x4y4+x2y2+xy) y dx +(x4y4-x2y2+xy) x dy=0.