### Problem Statement Find a function \( f(x, y, z) \) such that \( \nabla f \) is the constant vector \(\langle 7, 4, 3 \rangle\). (Use symbolic notation and fractions where needed. Use \( C \) for the constant of integration.) \[ f(x, y, z) = \underline{\hspace{50mm}} \]

Q: Let f(x) = f'( - π) = 9x sin x + cos x

A: The given function .We have to find the value of .

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A: Given that   u(x) = sin(x)    v(x) = x16   and f(x) = (u(x))/(v(x))

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Q: (c) (d) S. 25 ∞ 2x³ dx 1 -2x +4 dx

A: c) d)

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A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

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A: The solution is shown in step-2

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A: The solution is shown in step-2

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Q: Which function is represented by the graph below? 3+ 24 44 --24 -34

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A: The graph of the vectors  and  are given.We have to sketch the graph of the vector .

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A: To the 3rd term means upto 2nd derivative.

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A: If two vectors are orthogonal then the dot product of the vectors is 0.

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A: To find:The potential function. First we will show that F is conservativeThen finding the potential…

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A: Given:We are required to find:

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Q: d Use the Product Rule to find (and simplify): [sin'x]

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