4 4 Consider the function fx, y) = 4x*+ 4y* – 16xy + 3. Which of the following statement is true?

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

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Q: S (2y-3) dy 2y ³-y²-27y + 36

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Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* - 6x – 2y² + 1 (Express numbers…

A: Given function f(x,y)=x3+y4-6x-2y2+1

Q: Suppose that ∇fp =〈2, −4, 4〉. Is f increasing or decreasing at P in the direction v =〈2, 1, 3〉?

A: 1) v=2,1,3 v=22+12+33 = 14 u=vv=1142,1,3

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: I shift as in Example 4.9 to find the general solu b. (2D – 1)²y = 0 + czx?)e2x

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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: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

A:

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

A:

Q: 7. For what values of m does the function y = e™* satisfying the following equation y" – 3y' – 10y =…

A: We have to find the values of m.

Q: 11 9. | f(z)dz - f(2)dz = | f(#)dx %3D 4. 4 where a = and b = Question Help: DVideo M Message…

A: ∫411f(x)dx-∫45f(x)dx=∫abf(x)dx∫411f(x)dx+∫54f(x)dx=∫abf(x)dx∫511f(x)dx=∫abf(x)dxa=5,b=11…

Q: Let A = {x E Z: 8x} and let B={rEZ:12lx}. Then * ACB ВСА None of these A=B

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Q: Let f(x, y, 2) = xe' + ye" + ze* and P,(1,0,0) then Vfle, is 2i + 2j + k. True False

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Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: Which of the following is true if* f(x, y) = 2- 2xy + xy³ + 3y? frz (x, y) = 6x fyy (z, y) = 6+ 6xy…

A: Given that f(x,y)= x^3-2xy+xy^3+3y^2 then find the fxx, fyy, fxy.

Q: 7. If DE %3D 11x + 15 and FG 32x - 27, find x. %3D F D H.

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

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Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: If f(x,y,z) = In(xz) – 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D d) – 2 e) - 4 g) None of…

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Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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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: 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: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers…

A:

Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

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

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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: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Q₂. if z=f(x+ct) + g(x-(t) then show that C²Z = Ztt XX

A: Given function: z=fx+ct+gx-ct We have to prove that, c2zxx=ztt. We know that, daxndx=anxn-1

Q: 3 4 If f(x, y) = x3 + 5x?y + y3 and u = calculate Du?f(3, 1). 5' 5

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Q: 1. Given f(x, y) = 4x³y², evaluate f;(1, y) and fy(x, 2).

A: We know that partial derivative of f with respect to x is denoted by fx  and partial derivative of f…

Q: If f(2) = | * t3 dt then f'(x) = and f'(6) %3D Submit Question

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Q: Q3: 1f f(x, y) = 4xCy5 + 6x*y* .Prove that: f(x,y) * fxxyy fxx * fyy = 1

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Q: 3 ) If f:(1,00)→ [2, 00) is given by F(x)=Dx+, find f(x), (assume bijection).

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Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

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

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Q: 7 Suppoe | f(x) dæ = 3, f(x) dx = 14, | f(æ) dæ = 7. %3D Then 8. f(x) dx Σ I F(x) dzæ = Σ

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Q: O show thet fu) =2a +3b is Candin Uous where a, b are Constants.

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Q: find af/ax and ðf/əy +4- 17. f(x, y) = sin² (x – 3y) %3D

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Q: 9. Find fx and fy and f; for f(x,y,z) = (x² + y² + z²)~1/2 %3D

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Q: 2s If F (s) = (s+1)2 then

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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: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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Q: If f(x,y)=x2+2y2, then fx(2,1) and fy(2,1) are...

A: f(x,y)=x2+2y2,find fx(2,1) and fy(2,1)

Q: If f(x,y,z) = In(xz) - 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D -3 d) – 2 e) - 4 g) None…

A: ANSWER

Q: If f(x1..... ,e) =g(6,0) h(x,.. ), then %3D Select one: a. consistent b. efficient C. sufficient d.…

A: sufficient estimator:-An estimator "θ^" is said to be a sufficient estimator for θ if it containsall…

Q: 2 [² fo Given f(x,y) = x²y-3xy³. Evaluate fdy

A:

Q: 11 f(x,y) 3x-7y+2, R is the rectangle with opposite car- ners (-1,0) and (1,3).

A: 12. Given: fx,y=2x+2y+2 and triangle with corner 0,0 To find the area of the triangle. The formula…

Q: If f(x, y) = = Select one: O True O False x² + 2xy + y³ 2x + 2y 3y² + 2x '(x² + 2xy + y³)²¹ (x² +…

A: As we know the expression for ∇fx,y. ∇fx,y=i∂∂x+j∂∂yfx,y=∂fx,y∂xi+∂fx,y∂yj   Given: fx,y=1x2+2xy+y3

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

A: