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Q: 9. If f(x, y) = x³ + 4xy² + y3 %3D show, that f (ax, ay) = a³f (x,y) %3D

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Q: Let f(æ, y) axy + az?y+ y³. (a) div(grad(f)) = (b) Find a so that div(grad(f)) = 0 for all æ, y. %3|…

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Q: If f(x, y) = xsec²2y + ycosec²2x + 2xy then show that, drdy dydx

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Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

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Q: Suppose that f(x, y) = e-2r² – 1y² + 2x +8y then find the discriminantD= faz fyy – fay- Question…

A: Solution: The objective is to find the discriminant

Q: af If f(x) = x²yz + xy³z than is дудz x?yz + xy°z yz + y°z Option 1 Option 2 x? + 3xy? y? + 3xy?…

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Q: Find Duf at P. 2 + 2. 5,3 4 f(x, y, z) = 6x³y°z*; P(1, – 2, 1); u = Duf i

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Q: B. Obtain PDE by eliminating the arbitrary functionsfrom the following; 2. Ix + my + nz = Ø (x2 + y?…

A: Partial differential equation by eliminating arbitrary function

Q: Let f(x, y) = 9e2xy what is fxyx (x, y) =? %3D Select one: O a. 72ye2xy + 72xy²e2xy O b. 36хуе2у +…

A: Given: f(x,y)=9 e2xy ; To find the value of fxyx(x,y)=?

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: b) Find the orthogonal traJec tories of the families o f r=5acose where la) parameter

A: We have to find the orthogonal trajectories of the families of r=5acosθ where a is parameter.

Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: Find the maxium andd minimum values of the following functions by using Lagrange Multiplier. a) f(x,…

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Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: It is always the case that f(x, y) dydx = f(x, y) dædy. OTrue False

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Q: If f(x, y) = 8xey + 8y Inx, then is given by:

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Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: If S(x, y)= x² +y , find f, and f, . %3D Vr

A: Fx is partial differentiation of F with respect to x.

Q: Let f(z) = kz5 + az + cz. Find v(x,y) if z = 6.3 + 3.3i, a = 8, c = 12, andk = 5. Round off vour…

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Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Consider f(x, y) = x³ + 2ry + y. Compute the following: (b)

A: Answer and explanation is given below.. Simply do partial derivative with respect to x and y.

Q: Find as a function of (s, t)when z = r° = 3ry+ 6, x = st, y= 2t² O = 3st2 - 6t2 - 3st %3D O. 3st…

A: Note: Since you have posted multiple question. As per our guidelines we are supposed to solve one at…

Q: Determine the maximum and minimum values of f(x,y,z) = 3x + 6y + 2z, subject to 2x^2 + 4y^2 + z^2 =…

A: Using the lagrange multipliers

Q: x2 B) If w = x".f then show that: %3D x. Wx + y. Wy = nw.

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Q: If h(z) = 2 – 4, find h(z). %3D

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Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: Use Lagrange multiplier to find the indicated extrema, assuming that x and y are positive. 6.…

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Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

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Q: If s 3/t + 2, then || ds (3sqrt(t)+2)/x Preview dt

A: Given: s=3t+2          dsdt=d(3t+2)dt                 =d(3t)dt+d(2)dt…

Q: WAS Given f(x, y) = 5x + 4x*y° - 6y°, find 13 f-(x, y) = | f,(z, y) = %3D faz (a, y) = %3D fay (2,…

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Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: Q4. Find guerel polution of following systens uning either method' of undetermind coefticients or…

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Q: For the function f(x,y,z) = In (5x + 7y+ 9z), find fx, fy, and fz.

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Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: Given f(r, y) 2x* + 4x²y² – 5y°, find fz(x, y) - fy(x, y) = fzz(T, y) = fzy(T, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 9. Find y if (a) y = 2" In (cot² (v7))

A: We are authorized to solve only one independent question, please repost remaining questions…

Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: Consider f (x, y) = re63ry f-(x, y) = e63ry and fy(x, y) = %3D e63ry

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Q: Use the False Position method to find an approximation to the value of v7 that is accurate up to…

A: False position method formula x2=x0-f(x0)⋅ x1-x0 f(x1)-f(x0)

Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

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Q: find equateons of the Jangent knes to the Cure. X-1 trat are fardllelb the line x-2Y=5 Smaller Y-…

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Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.