Exam 12: Section 2: Vector-Valued Functions

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Find Find   given the following.  given the following. Find   given the following.

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Find the indefinite integral below. Find the indefinite integral below.   Do not include an arbitrary constant vector. Do not include an arbitrary constant vector.

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Find the indefinite integral below. Find the indefinite integral below.   Do not include an arbitrary constant vector. Do not include an arbitrary constant vector.

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Use the properties of the derivative to find Use the properties of the derivative to find   given the following vector-valued functions.  given the following vector-valued functions. Use the properties of the derivative to find   given the following vector-valued functions.

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Find the indefinite integral below. Find the indefinite integral below.   Do not include an arbitrary constant vector. Do not include an arbitrary constant vector.

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A particle moves in the yz-plane along the curve represented by the vector-valued function A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   . . Find the minimum value of A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   . .

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Use the properties of the derivative to find Use the properties of the derivative to find   given the following vector-valued functions.  given the following vector-valued functions. Use the properties of the derivative to find   given the following vector-valued functions.

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Evaluate the definite integral below. Evaluate the definite integral below.

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Find Find   given the following vector function.  given the following vector function. Find   given the following vector function.

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Find Find   given the following vector function.  given the following vector function. Find   given the following vector function.

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Find the vectors Find the vectors   and   for the following vector function.  and Find the vectors   and   for the following vector function.  for the following vector function. Find the vectors   and   for the following vector function.

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Find Find   given the following vector function.  given the following vector function. Find   given the following vector function.

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A particle moves in the yz-plane along the curve represented by the vector-valued function A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the maximum value of   . . Find the maximum value of A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the maximum value of   . .

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Evaluate the definite integral below. Evaluate the definite integral below.

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Find Find   given the following vector function.  given the following vector function. Find   given the following vector function.

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Find Find   given the following.  given the following. Find   given the following.

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Use the properties of the derivative to find Use the properties of the derivative to find   given the following vector-valued functions.  given the following vector-valued functions. Use the properties of the derivative to find   given the following vector-valued functions.

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Find Find   given the following vector function.  given the following vector function. Find   given the following vector function.

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Find the open interval on which the curve given by the vector-valued function Find the open interval on which the curve given by the vector-valued function   is smooth. is smooth.

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Find Find   given the following vector function.  given the following vector function. Find   given the following vector function.

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