Determine if the function f (x, y) = if (x, y) = (0,0) is continuous at (x, y) = (0,0). If not, classify the type of discontinuity 1-√√x² + y² + 1 x² + y² 1 -, if (x, y) = (0,0)

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A: It is given that, fx,y=xy-x2-y2-3x-3y+12We have to find the local extreme values.

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Q: Let f(x, y) = 125-3x²-2y2² Evaluate f(0, 3)

A: f(x,y)=sqrt(125-3x2-2y2)Find f(0,3)

Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

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Q: Apply Rolle's theorem for the function f(x)-x2+2x over the interval [-2,0]. Justify your answer.

A: Rolle's theorem is used to prove the Taylor's theorem and the mean value theorem. Rolle's theorem…

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Q: Identify and sketch the domain of f(x, y) = 4x² In x Y

A: For function to be valid denominator must be non zero and log has non-negative real numbers and…

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Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: Q21) One of the following is correct for functions the f(x)=1,g(x)= x³ and h(x) = ln(x): a) f(x),…

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Q: Determine if F = x²yî + (xyz +29)ĵ – x²y²k is conservative or not %3D

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A: Given: Figure of the function :

Q: A competitive firm's profit is given by T(x,.x2) = 95(4x2 + 6x}")- 4.75x, - 15x2. %3D The stationary…

A: To find stationary point of a function fx,y, we have to find fx and fy. Then we put fx=0 and fy=0.…

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Q: Find the maximum and minimum values of f(x) = x3 − 6x2 + 8 on the horizontal span of 0 to 10.

A: We're tasked with finding the maximum and minimum values of the function f(x)=x3−6x2+8 over the…

Q: Let f(x, Evaluate f(3, 4) y)=√150 - 4x² - 2y²

A: fx, y=150-4x2-2y2

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A: we have to check if the function  f(z)=y+xi

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A: Given data:- The given function is, fx=x+1

Q: Find a,b to continue the function at x=3 if: x > 3) x = 3 x < f(x) = ax + b 2ab + 1 bx - a +3 3)

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Q: Identify and sketch the domain of f(x, y) √x-y In (1 + y - x²)

A: ,

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

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Q: A competitive firm's profit is given by 7(x,, x2) = 95(4x2 + 6x)- 4.75x,- 15x,. %3D The stationary…

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