Determine the set of points at which the function is continuous. ху if (x, y) + (0, 0) f(x, y) = + xy + y2 if (x, y) = (0, 0) y)\x > and y > o {(x, v)\x ER and yER}

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

Q: find the absolute extrema of the function f(x) = x^2 - 6x on the intervals [- 1,6], (3,7], (0, 6),…

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Q: Find the absolute maxima and minima for f(x) on the interval [a, b]. f(x) = x3 - 6x2 - 36x + 5, [-3,…

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: oints, where the function f ఐ,00)

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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: 9. What is the domain of the function f(x) = Vx- 3? | A. (3, 0) B. (-00, 3] С. [3, о) D. (-00, 3)

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Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

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Q: Show that if f (x, y, z) = 0 then = -1.

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Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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Q: Study the continuity of the next function x²y² x²y² + (x - y)² 0 - f(x, y) = if (x, y) = (0,0) if…

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Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

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Q: Let f(x, y) = Evaluate f(5,5) 175 - 3x² - 4y2

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Q: How.L Find minima, bmakima and Saddle paints for the functionss foxy) -9x -4 xy 3- %3D f Cx,y) = 2…

A: (3) the given function is fx,y=9x3+y33-4xy Now we have to find ∂f∂x,∂f∂y,∂2f∂x2,∂2f∂y2 and ∂2f∂x∂y

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: Use implicit differentiation to find dy/dx 4G - y = 2x = 2- 4y dx O dy. 2-dy dx

A: It is implicit derivative.