Let be the hemisphere x 2 + y 2 + z2 = 50, z > 0 and suppose f  is a continuous function with f (3, 4, 5)=7 f (3, -4, 5 ) =8 f (3, 4, 5 )=9 and f (3, 4, 5)=12 By dividing into four patches, estimate the value of xxH f x, y, z dS

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

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Q: f 'C) =7x*+7-3 ond fl0) 3D8

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Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

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Q: Is 6y-y^2 a convex function

A: Given:  Let fy=6y-y2  To Find: To check the given function for a convex function.

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A: f'(c) = f(b) -f(a) /b-a

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: