Exam 15: Section 2: Vector Analysis

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Find the area of the lateral surface over the curve C in the xy-plane and under the surface Find the area of the lateral surface over the curve C in the xy-plane and under the surface   where Lateral surface   .   line from   . where Lateral surface Find the area of the lateral surface over the curve C in the xy-plane and under the surface   where Lateral surface   .   line from   . . Find the area of the lateral surface over the curve C in the xy-plane and under the surface   where Lateral surface   .   line from   . line from Find the area of the lateral surface over the curve C in the xy-plane and under the surface   where Lateral surface   .   line from   . .

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Evaluate the integral Evaluate the integral   along the path C, defined as   from  along the path C, defined as Evaluate the integral   along the path C, defined as   from  from Evaluate the integral   along the path C, defined as   from

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Find the work done by the force field Find the work done by the force field   on a particle moving along the given path.   from   to   . on a particle moving along the given path. Find the work done by the force field   on a particle moving along the given path.   from   to   . from Find the work done by the force field   on a particle moving along the given path.   from   to   . to Find the work done by the force field   on a particle moving along the given path.   from   to   . .

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E

Find a piecewise smooth parametrization of the path C given in the following graph. Find a piecewise smooth parametrization of the path C given in the following graph.

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Evaluate Evaluate   along the path C, defined as y-axis from   . along the path C, defined as y-axis from Evaluate   along the path C, defined as y-axis from   . .

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Find the work done by the force field Find the work done by the force field   on a particle moving along the given path.     from (0,0) to   . on a particle moving along the given path. Find the work done by the force field   on a particle moving along the given path.     from (0,0) to   . Find the work done by the force field   on a particle moving along the given path.     from (0,0) to   . from (0,0) to Find the work done by the force field   on a particle moving along the given path.     from (0,0) to   . .

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Evaluate Evaluate   where C is represented by   .  where C is represented by Evaluate   where C is represented by   .  . Evaluate   where C is represented by   .

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A tractor engine has a steel component with a circular base modeled by the vector-valued function A tractor engine has a steel component with a circular base modeled by the vector-valued function   . Its height is given by   . (All measurements of the component are given in centimeters.) Find the lateral surface area of the component. Round your answer to two decimal places. . Its height is given by A tractor engine has a steel component with a circular base modeled by the vector-valued function   . Its height is given by   . (All measurements of the component are given in centimeters.) Find the lateral surface area of the component. Round your answer to two decimal places. . (All measurements of the component are given in centimeters.) Find the lateral surface area of the component. Round your answer to two decimal places.

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Find a piecewise smooth parametrization of the path C given in the following graph. Find a piecewise smooth parametrization of the path C given in the following graph.

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Evaluate Evaluate   along the path C, defined as counterclockwise along the circle   from   to   . along the path C, defined as counterclockwise along the circle Evaluate   along the path C, defined as counterclockwise along the circle   from   to   . from Evaluate   along the path C, defined as counterclockwise along the circle   from   to   . to Evaluate   along the path C, defined as counterclockwise along the circle   from   to   . .

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Evaluate Evaluate   where   and   . where Evaluate   where   and   . and Evaluate   where   and   . .

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Evaluate the integral Evaluate the integral   along the path C, defined as y-axis from   . along the path C, defined as y-axis from Evaluate the integral   along the path C, defined as y-axis from   . .

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Evaluate the line integral along the given path. Evaluate the line integral along the given path.

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Find the total mass of the wire with density Find the total mass of the wire with density   .  . Find the total mass of the wire with density   .

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Find the moments of inertia for a wire that lies along Find the moments of inertia for a wire that lies along   with density   . with density Find the moments of inertia for a wire that lies along   with density   . .

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Evaluate Evaluate   where C is represented by   .  where C is represented by Evaluate   where C is represented by   .  . Evaluate   where C is represented by   .

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Find the work done by a person weighing Find the work done by a person weighing   pounds walking exactly one revolution up a circular helical staircase of radius   feet if the person rises   feet. pounds walking exactly one revolution up a circular helical staircase of radius Find the work done by a person weighing   pounds walking exactly one revolution up a circular helical staircase of radius   feet if the person rises   feet. feet if the person rises Find the work done by a person weighing   pounds walking exactly one revolution up a circular helical staircase of radius   feet if the person rises   feet. feet.

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Evaluate the line integral along the path C given by Evaluate the line integral along the path C given by   , where   .  , where Evaluate the line integral along the path C given by   , where   .  . Evaluate the line integral along the path C given by   , where   .

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