5. Use the energy method to prove the uniqueness of the solution for the problem 0< ¤ < L, t > 0 t> 0 U = kurg + h(x, t) u(0, t) – au,(0, t) = A(t) u(L,t) + Buz(L, t) = B(t) u(x, 0) = f(x) |3| t> 0 0 < x < L where o, B20 and k > 0.

Q: .4 || (cos²e + sin?e) dp dz de 8 2(0*cos?8 + p*sin?e) p dp dz de

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Q: 5. Suppose z=f (x,y), where x=g(s,t)and y=h(s,t). Show that Oz d'x, z 0y +. 生() az ôx ôy d:(dy +2-…

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Q: 1. Let z = f(x, y) = -tan x + y² + eysin. (a) Use local linear approximation to approximate the…

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Q: 5. Solve V'u = 0 0<r<1 [1 u(1,4) 0 < 0 < T/2 T/2 < 6 < T -1 This is the problem where the boundary…

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Q: Find the functions x*(r) and y*(r) such that x = x*(r) and y = y*(r) solve the problem max f(x, y,…

A: max fx , y, r=max-x2-xy-2y2+2rx+2ry To Find: x*r , y*r such that x=x*r ,y= y*r.

Q: Let y' = y(y-3) Use Euler's method to approximate y(1) for the function y satisfying y'=y(y-3) and…

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Q: Let f(x, y) = x³ + y³ - 2x²y². Calculate fa, fy, fax, fyy and fry. Hence show that (3/4, 3/4) is a…

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Suppose that you have the utility function: u (x) = Vx u" (x) 43 %3D Find : u' (x) 1 2x 2x Option 2…

A: I have stated the used formulas in the solution

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Q: 3. Find and classify any potential extrema of the function (i.e. first and second derivative test)…

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Q: Show solution using Heaviside function

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Q: c'(x) = e(x) e'(x) = t(x) t'(x) = h(x) h'(x) = c(x) 0 1 2 1 0 4 3 3 4 1 2 لا e(x) c(x) 3 t(x) 4 1 3…

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Q: Consider y" + 4y' + 5y = ae -3* 8 (t - 31), y (0) = 1, y (0) = -2. Зл Find the value of a such that…

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

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Q: Solve PDE 1 = e=*t u. u̟ =e¯*t Xx k (o0) u(0,t) =0 u(L,t) = 0 u(x,0) = L -x?

A: The given PDE is,uxx-1kut=e-xt

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Q: 2) a) Find the general antiderivative of the function f(x) = 5 (2x + 1) - x+ x2 + 1 ANTIDERIVATIVE :…

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Q: What is the maximum rate of change of ƒ(x, y) = x² + y² at the point (1,0) ○ (2,0) 2x + 2y 4x² + 4y²…

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Q: Recall that u(x, t) = } + So" V32 e-r dr solves Ut subject to u(x, 0) = H(x) where H(x) is the…

A: Please check step 2 for the solution.

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A: Given fx=2-3x given interval 1,3 f'c=f3-f13-1

Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

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Q: 8. The velocity of a particle moving along a straight line at time t is given by v(t) = 2t – 2t3/2 –…

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Q: Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations: C(t) +…

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Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

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Q: Find T3(X). (a) f(x, y) = e* cos y, Xo = (0,0) %3D %3D

A: As per Bartleby guidelines, for more than one question asked, the first is to be answered. Please…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.