Exam 12: Section 1: Vector-Valued Functions

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Find Find   given the functions below.  given the functions below. Find   given the functions below.

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E

Evaluate the limit given below. Evaluate the limit given below.

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B

Find the domain of the vector-valued function given below. Find the domain of the vector-valued function given below.

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C

Determine the interval on which the vector-valued function Determine the interval on which the vector-valued function   is continuous. is continuous.

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Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter    Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter

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Find Find   given the function r(t) below.  given the function r(t) below. Find   given the function r(t) below.

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Find the domain of the vector-valued function given below. Find the domain of the vector-valued function given below.

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Evaluate the limit given below. Evaluate the limit given below.

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The graph below is most likely the graph of which of the following equations.. The graph below is most likely the graph of which of the following equations..

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Sketch the curve represented by the vector-valued function Sketch the curve represented by the vector-valued function   and give the orientation of the curve. and give the orientation of the curve.

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Suppose the two particles travel along the space curves Suppose the two particles travel along the space curves   and   . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision. and Suppose the two particles travel along the space curves   and   . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision. . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.

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Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter    Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter

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Match the equation with the graph shown in red below. Match the equation with the graph shown in red below.

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Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter    Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter

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Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter    Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter

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Given the vector-valued function below, evaluate Given the vector-valued function below, evaluate   .  . Given the vector-valued function below, evaluate   .

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Represent the following curve by a vector-valued function. Represent the following curve by a vector-valued function.

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Find Find   given the function r(t) below.  given the function r(t) below. Find   given the function r(t) below.

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Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.

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Evaluate (if possible) the vector-valued function at the point given. Evaluate (if possible) the vector-valued function at the point given.

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