QI. Solve the following problem with insulated boundaries: U = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x, 0) = f(x) P.D.E. 0

Q: Find the extrema for the function: = f(x,y) = x²y2 - x² – 3y3 %3D

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Q: IX. Į F dF where F = (x,y) and C is the straight line from (2,3) to (4,0)

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Q: At what interval is y=2x4-4x2 concave upward? 3 3 3. V V V

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Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: Show that the function y = x1/2, x > 0, is strictly concave

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Q: Find the point on y = 4+ x² that is closest to (1, 1). 0 (0,4) O (0.142, 4.020) O (0.545, 4.194) O…

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Q: Evaluate the value of I = (4,0). I = Sleby. r 3x) dx + (6xe6y + y)dy, where I is the straight line…

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Q: Choose the correct answer     If A = {x: 0 <x <2} and B = {y: O <y <1/2) Find C = AU B and D = A…

A: Provided information is ; A = {x: 0 &lt;x &lt;2} and B = {y: 0 &lt;y &lt;1/2) we know that ; AUB =…

Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

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Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

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Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: Given A = A(x, y) subject to bzx+ byy <B and Cxx+ Cyy <C i) Write the Lagrangian function. ii) Write…

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Q: 64. Business: growth of an investment. A company deter- mines that the value of an investment after…

A: Consider the given curve. Vt=5t3-30t2+45t+5t   (A) Graph V over the interval 0, 5

Q: af and . Given f(x, y) x'+ y find dx ' dy' axdy дудх

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Q: The internal energy U of a gas can be expressed in the form U=f(p,V,T) with variables defined by: p…

A: Step 1:Use Ideal gas Law;PV=nRTInternal energy can be related to ideal gas…

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

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Q: For which value(s) of a and b is y = abx concave up? b>1, a<0 00 0<b<1,a<0 b>1,a>0

A: We have find correct option

Q: 14. We know that S(x,y)dx+g(x,y)dy] = Se f(x,y)dx + Se g(x, y)dy. Use this knowledge to evaluate S.y…

A: We integrate this by making two path where for one path only y vary and for other path only x vary.

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: 1. Let f(u, v) be a continuously differentiable function. Let u = e*, v = e³. Show that u²fuu + v²…

A: Given that f(u,v) is a continuously differentiable function, and u=ex, v=ey then show that…

Q: Find the pro ection of v on the line with equation

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Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: The density of air changes with height. Under some conditions density p. depends on height z, and…

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution