Does the following function satisfies the symmetry condition? a(v, u) = f(vxK Ux +vAu)dx -1

Q: Let I = f x*cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: B) Use Green's Theorem to evaluate F dr, where C is the triangle with vertices (0,0) (3,0) and (3,…

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Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: The speciat sotution to the equatio %3D ho A/y)=+X B/yo)=y - %3D d/other than that

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Q: Consider the function f defined on [0, 1] such that f(0) = 1, ƒ(1) = 3, f(1/5) = f(3/5) = S, f(x)dx…

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Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

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Q: Consider f(x, y) = x³y+ 2xy? Approximate f(2.1, 1.03) by using the tangent plane.

A: Given f(x, y) = x³y + 2xy² Find f(2.1, 1.03) using tangent plane.

Q: Consider the function f(x, y) = ax – 2y + 1 where a is a positive number. S SR ax 2y + 1 dA = 45,…

A: A double integral involves the integral with respect to the product of any of two variables in x,y,…

Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: Given f(x, y) = et" Y° – a°y°, show that fæy = fyx· 93 fyæ- %3D

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Q: Show that u(x, y) is harmonic in some domain. u(x, y) = 2x – x³ + 3xy?

A: since Uxx+Uyy=0, then U is harmonic

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Given that F = (2x + y2)i + (3y – 4x)j. Verify Green's theorem for F.dr around the triangle formed…

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Find a function u = u(x, t) that satisfies the PDE Uxx = 0, subject to the boundary conditions 0 0,…

A: Consider the given differential equation, uxx=0, 0<x<1, t>0 The auxiliary equation of the…

Q: Find the following for z = f(x, y) = x? +5x2y3-y. az %3D ax

A: FOLLOW NEXT STEP

Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x-…

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Q: Show that the Cobb-Douglas function F(x, y) = bx" y" satisfies the equation ƏF ƏF + y (n + m)F(x, y)…

A: Given that the Cobb-Douglas function F(x,y)=bxnym We have to satisfies the equation…

Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

A:

Q: Find the value of c such that the regionbounded by y = c sin x and the x-axis on the interval [0, ∏]…

A: Given y = csinx and the region bounded by y = c sin x and the x-axis on the interval [0, π] has area…

Q: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: S F(2,v) For any function f(x, y) continuous on the ry-plane, f(r, y) dædy. O True False

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Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: Let Y be a function of the RV X as follows: YA SX, x², x Compute fy (y) in terms of fx (x). Assume…

A: Given that fX(x)=12πe-12x2   If Y=X, then  fY(y)=12πe-12y2         =12πe-12x2

Q: The harmonic function for f(z) = u(x,y) + iv(x,y) to be analytic are:

A: Given that: f=u+iv

Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

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Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

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Q: The function f(z) =e² is: contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y) =e*sin(y)

A: The function f(z)=ez the given function is continuous.

Q: Show that the function u = p(ry) + JFÿ¢(y/x) provides the quation „Pu = 0. dy

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Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

Q: Consider z = Ax + By + D be the tangent plane to f(x, y) = 2x² + 5y³ + 9xy + 9x + 3y at (6,9).What…

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Q: . Show that the function u = p(ry) + Vry v(y/x) provides the quation = 0. ду? %3D dx²

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Given f(æ, y) = e"" Y' – z°y", show that fæy = fyæ.

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Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: If y (x, t) is a function of x and t, prove that i) Lat =py (x, p)- y (x, 0) ii) L- = p°y (x, p) –…

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Q: 8. For f(z) = e², find arg f'(z). Use this to verify that lines parallel to the y axis and x axis…

A: Given: f(z)=ez To find: arg(f'(z)) To verify that lines parallel to y-axis and x-axis are mapped…

Q: Suppose that f(0) = 1, f(0.5) = 2.5,f(1) = 2, and f(0.25) = f(0.75) = a. Using trapezoidat rule with…

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Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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Q: Evaluate fy and f, at the given point. f(x, y) = e³Y sin(x), (T, 0) fx(T, 0) fy(T, 0) %3D

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Q: Given the interval [a,b] that saitisFies the hypothesis of Rolle's Theorem For the Furnction f(x) =…

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Q: b. What is fo, f (z) dz?

A: f(z) is holomorphic except at z0   where f(z) has pole at z0 we can write  f(z)=g(z)z-z0  where g(z)…

Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

A: