Question 8. Consider the function g defined by g(x, y) = e^y(y − x^2) for all real x, y. Which of the following terms are needed to represent the length of the gradient ∇g(1, −1) ? a) √10 b) √5 c) e d) π

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A: This is a problem of Vector Calculus.

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A: Given that  fx,y = xy ,  P  0, -1   and  v = 3 i + 3 j (a)  The gradient of f is  grad f or  ∇f =…

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A: Scalar integrable  function y = f (x)

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A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve first three…

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Q: please see image

A: Taking the cues from hint in the question:

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A:

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A: Explanation of the solution is given below....

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Q: The gradient of the lcalar function f= x²+y2+z²is. fa) xityj+zk tyjt +龙ん

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A: Since you have posted a question with sub-parts greater than three. We will provide the solution…

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