Let f(x,y) = x - 5xy -y². Compute f(6,0), f(6, – 2), and f(b,c).

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Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Let f(x,y)=-x³+4xy-2y²+1; find the critical points of f and test them using D=D(x,y).

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Q: Let f(x,y) = x² – 8x + 2y² + 4y + 7. a. Find and classify all critical points of f.

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

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A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

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Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

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Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: .Determine if F(x, y) = (2xy + y-2)i + (x² – 2xy-3)j for y > 0 is conservative.

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Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: xy ) Suppose thot fixy)=e , x(4,0)= 3uSiina, glu, vl = f(x (4,v), yluiv), find , by using Chain Rule

A: Using the chain rule,

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

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Q: For the function f(x, y, 2) = 102° y³z+ 7æy®z4 + 19xz2 + 8y%z4 + 5a° + 17y7a11 + 4xyz +23 compute…

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Q: Let f(x, y) = xy+ + 2x²y + 4y5 (a) Find fr- (b) Find fy-

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Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

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Q: Let f(x, y) = 4x² + 5xy + 2y? – 2x – 3y +1. Find all critical points, and state what type they are.

A: Given: f(x, y)=4x2+5xy+2y2-2x-3y+1 We have to find all the critical points and state their type.…

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

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Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Let f(x, y) = 8+ 76xy+38x2 + 240y + . Find and classify the critical points of f.

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Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = 3x - 4y + 5 at a. (0, 0), b.…

A: fx, y=3x-4y+5 Partially differentiating with respect to x, we get fxx, y=31-0+0=3 Partially…

Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…

Q: show that the L operator is linear for y" – 4y" + 2y' + y = x2

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