(a)Show that F is a conservative vector field. f(x,y,z) = < yzcos(xz)-y^(2), sin(xz) - 2xy, 3z^2 + xycos(xz) > (b)Find a potential function for F.

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A: We have find the solution

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A: We can find the answer as below.

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A: I have stated the used formulas in the solution

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A: To find out the correct linear equation which is shown in the graph below.

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A: From the given graph we can notice that the line passes through origin.

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A: Please see the below picture for detailed solution.

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A: We can find the answer as below.

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A: The objective is to find the limit.

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A: As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And the common…

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

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A: Topic = Derivative

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A: To evaluate the integral.

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A: Let's find inverse laplace of given function.

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A: We have to interval of convergence

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A: Solved below

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A: Given: 1,0,0 x=t+! y=-2t z=-3t

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

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A: We know that, A function, in mathematics, an expression, rule, or law that defines a relationship…

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A: Please see the below picture for detailed solution.