F(x, y) = (1 − e¯¤x)(1 – е¯³µ), for x ≥ 0, y ≥ 0 and a, ß > 0.

Q: If f(x,y)=xe/2+118x?y, then asf at (1,1) is equal to əx²əy³

A: Given function is: f(x,y)=xey22+118x2y3 Derivative of function with respect to 'x'…

Q: Solve for a2f дхдz if f (x, y, z) = x³=3y

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Q: (x, y, z) = 2x²y — xz² + 3y²z. Xyx

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Q: If f(x, y): X 2y + 1 use the definition to find af (x, y) ду

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Q: , (х, у) (0,0) x+y f(x.y)%3D (х, у) (0,0)

A:

Q: f(x)= x2/5 Where it concave up/down?

A: To find the concavity of the given function.

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

A:

Q: f(x y, z) = x2 - 8y5 + z -4. Find (-3, 1, 5) for O a 1 O b -4 10 O d -5

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Q: Find the mean value of the function f(X,Y)= X² + y².

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Q: Let f(x, y, z) = x³ + 5x²yz + 3xz+ 3, v = Then: D, f(a) = 201 0 -2 and a = -5 2 -5

A: Given that f(x, y, z) =x3 +5x2 y z +3xz+3 The directional derivative is a concept from multivariable…

Q: Suppose that 2x² - y² = t² and x = t cos 0. Find (a). ¹(2), X and 0

A: answer is in next step

Q: Calculate fx(l, 3) and /y(l, 3) for f (x, y) =

A: Given: fx,y=7x+y2

Q: then If f(x,y)= x²y+ y, 3x O b. бху 6x O d. o

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Q: y = v1- x+ x2 ||

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Q: For f(x, y, z) = x² - y² + z², find f(2, -1, 4).

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Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

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Q: g(x,y) = sq root of (5xy - 3x) find gx and g

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Q: For the function z = - 8x³ - 2y² - 2xy, find a z(1,-2), andz(1,-2). dz dz a ax' dy ax

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Q: If z varies direct to the square of y and y varies inverse to x (x,y,x) = (20,120,100) Then find the…

A: z varies directly to the square of y, so z=my2 y varies inversely to x, so, y=nx Therefore,…

Q: Normalize (z) = 3f2(x) +2f3(x). You can think of functions being 0 beyond the [0, L] interval, where…

A: Simple Linear Scaling:If f2(x) and f3(x) are linear functions that map the [0, L] interval to [a, b]…

Q: aff (² Find (3x + 2y)dA where D = {(x, y) | x² + y² ≤ 25, x ≥ 0}

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Q: Find fry (1,2) for f (x, y) = y?ln(7 + x) +. 23 41 -- 4 23 41 4 27°C Rain showers

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Q: Find a local linear approximation for the function f(x)=2x+8/x−2 valid for x near 3  2x+8/x−2≈

A: Linear Approximation: The formula for the local linear approximation of a function fx is given by,…

Q: Given f(x, y) = 2x4 - 3xy³ - y, find fz(x, y) = fy(x, y) =

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Q: If f(x, y) = x³y + 9xy“, find the following. f(x, у) əx? |(1, 1)

A: