Determine if F is conservative, if it is then find a potential function. (a) F =< 2x + ye", 2y + yeª > (b) F =< y,x, z² > (c) F =< cos z, 2y, –x sin z >

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A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

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A: As per the rules we can answer only the first question and rest can be reposted.

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Q: Fundamental Theorem: 2z Let f(x) = | Vcos t + t° dt . Find the value of f'(x). %3D 1

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Q: Exercise 4. Show that the function f is not differentiable at (0,0) f(x, y) = x³ + y³

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A: As per our company guidelines we are supposed to answer 1st question . Kindly repost the others in…

Q: Find the derivative of the function. g(u) = (8+ u²)*(1 – 5u²)8 %3D = (n), 6

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Q: 2. (a) Show that F = (e² cos(y), –E sin(y), 2) is conservative using partial derivatives. (b) Find…

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Q: 3. Use the Fundamental Theorem of Calculus Part I to find the derivative of a) [(cost +r +e' )dt b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A: Given: fx,y,z=xy2z3 The gradient of a function if given by ∇f(x,y,z) =∂f∂x,∂f∂y,∂f∂z.

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Q: A) Find the linearization of the function at the given point. f (x, y) = 1+ y ln (6 – xy), at (5, 1)…

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Q: = ze'y = e+z'e= C to denote an arbitrary constant.)

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Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: af Consider the f unction g(t) = (², 2t) + 52(sin3t, t) express se ду g'(t) in terms of partial…

A: USE CHAIN RULE

Q: Can i get help with this problem step by step please?

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Q: 1. Find the gradient of the function f(x, y) = x² sin y.

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Q: A) Use the chain rule to find dt where wxty,x = sint + cost y cost- sint.

A: We will use chain rule to find the answer :)

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.