Exam 15: Section 1: Vector Analysis

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Determine whether the vector field is conservative. If it is, find a potential function for the vector field. Determine whether the vector field is conservative. If it is, find a potential function for the vector field.

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B

Find Find   .  . Find   .

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C

Find the divergence of the vector field. Find the divergence of the vector field.

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B

Find the divergence of the vector field F given by Find the divergence of the vector field F given by   . .

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Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)

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Find the divergence of the vector field at the given point. Find the divergence of the vector field at the given point.

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Determine whether the vector field is conservative. If it is, find a potential function for the vector field. Determine whether the vector field is conservative. If it is, find a potential function for the vector field.

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Find Find   for the vector field given by   . for the vector field given by Find   for the vector field given by   . .

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Find the conservative vector field for the potential function Find the conservative vector field for the potential function   by finding its gradient. by finding its gradient.

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Match the vector field with its graph. Match the vector field with its graph.

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Sketch the vector field Sketch the vector field   . .

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Determine whether the vector field is conservative. If it is, find a potential function for the vector field. Determine whether the vector field is conservative. If it is, find a potential function for the vector field.

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Find Find   .  . Find   .

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Sketch several representative vectors in the vector field given by Sketch several representative vectors in the vector field given by   . .

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Find Find   .  . Find   .

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Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.)

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Find the curl for the vector field at the given point. Find the curl for the vector field at the given point.

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Determine whether the vector field is conservative. Determine whether the vector field is conservative.

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Find the divergence at Find the divergence at   for the vector field  for the vector field Find the divergence at   for the vector field

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Compute Compute   for the vector field given by   . for the vector field given by Compute   for the vector field given by   . .

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