Exam 13: Extension C: Vector Calculus

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Determine whether or not F is a conservative vector field.If it is,find a function f such that Determine whether or not F is a conservative vector field.If it is,find a function f such that    Determine whether or not F is a conservative vector field.If it is,find a function f such that

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Suppose that F is an inverse square force field,that is, Suppose that F is an inverse square force field,that is,   where   Find the work done by F in moving an object from a point   along a path to a point   in terms of the distances   and   from these points to the origin. where Suppose that F is an inverse square force field,that is,   where   Find the work done by F in moving an object from a point   along a path to a point   in terms of the distances   and   from these points to the origin. Find the work done by F in moving an object from a point Suppose that F is an inverse square force field,that is,   where   Find the work done by F in moving an object from a point   along a path to a point   in terms of the distances   and   from these points to the origin. along a path to a point Suppose that F is an inverse square force field,that is,   where   Find the work done by F in moving an object from a point   along a path to a point   in terms of the distances   and   from these points to the origin. in terms of the distances Suppose that F is an inverse square force field,that is,   where   Find the work done by F in moving an object from a point   along a path to a point   in terms of the distances   and   from these points to the origin. and Suppose that F is an inverse square force field,that is,   where   Find the work done by F in moving an object from a point   along a path to a point   in terms of the distances   and   from these points to the origin. from these points to the origin.

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Determine whether F is conservative.If so,find a function f such that Determine whether F is conservative.If so,find a function f such that    Determine whether F is conservative.If so,find a function f such that

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Let Let   where   Which of the following equations does the line segment from   to   satisy? where Let   where   Which of the following equations does the line segment from   to   satisy? Which of the following equations does the line segment from Let   where   Which of the following equations does the line segment from   to   satisy? to Let   where   Which of the following equations does the line segment from   to   satisy? satisy?

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Find a function f such that Find a function f such that   ,and use it to evaluate   along the given curve C.    ,and use it to evaluate Find a function f such that   ,and use it to evaluate   along the given curve C.    along the given curve C. Find a function f such that   ,and use it to evaluate   along the given curve C.    Find a function f such that   ,and use it to evaluate   along the given curve C.

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