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Write the equation Write the equation   in rectangular coordinates. in rectangular coordinates.

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The slope of the curve The slope of the curve   at   is which of the following? A)    B)    C)    D)   at The slope of the curve   at   is which of the following? A)    B)    C)    D)   is which of the following?


A) The slope of the curve   at   is which of the following? A)    B)    C)    D)
B) The slope of the curve   at   is which of the following? A)    B)    C)    D)
C) The slope of the curve   at   is which of the following? A)    B)    C)    D)
D) The slope of the curve   at   is which of the following? A)    B)    C)    D)

E) B) and C)
F) All of the above

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Find parametric equations for the curve Find parametric equations for the curve   . .

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blured image , where blured image ...

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Find parametric equations for the curve Find parametric equations for the curve   . .

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blured image (There ar...

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Write the standard equation for the ellipse with the following characteristics: center Write the standard equation for the ellipse with the following characteristics: center   , vertex   , and focus   . , vertex Write the standard equation for the ellipse with the following characteristics: center   , vertex   , and focus   . , and focus Write the standard equation for the ellipse with the following characteristics: center   , vertex   , and focus   . .

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Write the equation of Write the equation of   in polar coordinates. in polar coordinates.

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The surface area The surface area   of the surface generated by revolving the parametric curve   about the x-axis for   is given by the formula   . Compute the area of the surface generated by revolving the parametric curve   about the x-axis. of the surface generated by revolving the parametric curve The surface area   of the surface generated by revolving the parametric curve   about the x-axis for   is given by the formula   . Compute the area of the surface generated by revolving the parametric curve   about the x-axis. about the x-axis for The surface area   of the surface generated by revolving the parametric curve   about the x-axis for   is given by the formula   . Compute the area of the surface generated by revolving the parametric curve   about the x-axis. is given by the formula The surface area   of the surface generated by revolving the parametric curve   about the x-axis for   is given by the formula   . Compute the area of the surface generated by revolving the parametric curve   about the x-axis. . Compute the area of the surface generated by revolving the parametric curve The surface area   of the surface generated by revolving the parametric curve   about the x-axis for   is given by the formula   . Compute the area of the surface generated by revolving the parametric curve   about the x-axis. about the x-axis.

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Determine the standard equation of the parabola whose focus is the point Determine the standard equation of the parabola whose focus is the point   and directrix is the line   . and directrix is the line Determine the standard equation of the parabola whose focus is the point   and directrix is the line   . .

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Express the parametric curve by an equation in Express the parametric curve by an equation in   and    and Express the parametric curve by an equation in   and    Express the parametric curve by an equation in   and

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Find the arc length of the parametric curve Find the arc length of the parametric curve   . .

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The slope of the curve The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)   at The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)   is which of the following?


A) The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)
B) The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)
C) The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)
D) The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)
E) The slope of the curve   at   is which of the following? A)    B)    C)    D)    E)

F) A) and E)
G) A) and D)

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The equation of The equation of   in Cartesian coordinates is which of the following? A)    B)    C)    D)    E)   in Cartesian coordinates is which of the following?


A) The equation of   in Cartesian coordinates is which of the following? A)    B)    C)    D)    E)
B) The equation of   in Cartesian coordinates is which of the following? A)    B)    C)    D)    E)
C) The equation of   in Cartesian coordinates is which of the following? A)    B)    C)    D)    E)
D) The equation of   in Cartesian coordinates is which of the following? A)    B)    C)    D)    E)
E) The equation of   in Cartesian coordinates is which of the following? A)    B)    C)    D)    E)

F) None of the above
G) C) and D)

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A particle travels along the path A particle travels along the path   (where length is in feet and time is in minutes). Find the speed of the particle and compute its displacement and the distance covered during the first minute of its motion. (where length is in feet and time is in minutes). Find the speed of the particle and compute its displacement and the distance covered during the first minute of its motion.

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blured image ft/min, blured image ...

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Suppose that Suppose that   has polar coordinates   , where x and y are not both zero. Find the polar coordinates of the following.  A)    B)    C)    D)  has polar coordinates Suppose that   has polar coordinates   , where x and y are not both zero. Find the polar coordinates of the following.  A)    B)    C)    D)  , where x and y are not both zero. Find the polar coordinates of the following. A) Suppose that   has polar coordinates   , where x and y are not both zero. Find the polar coordinates of the following.  A)    B)    C)    D)  B) Suppose that   has polar coordinates   , where x and y are not both zero. Find the polar coordinates of the following.  A)    B)    C)    D)  C) Suppose that   has polar coordinates   , where x and y are not both zero. Find the polar coordinates of the following.  A)    B)    C)    D)  D) Suppose that   has polar coordinates   , where x and y are not both zero. Find the polar coordinates of the following.  A)    B)    C)    D)

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Find the area of the inner loop of Find the area of the inner loop of   .  . Find the area of the inner loop of   .

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The length of the parametric curve The length of the parametric curve   is which of the following?  A)    B)    C)    D)    E) The length integral cannot be computed analytically by the methods covered so far. is which of the following? A) The length of the parametric curve   is which of the following?  A)    B)    C)    D)    E) The length integral cannot be computed analytically by the methods covered so far. B) The length of the parametric curve   is which of the following?  A)    B)    C)    D)    E) The length integral cannot be computed analytically by the methods covered so far. C) The length of the parametric curve   is which of the following?  A)    B)    C)    D)    E) The length integral cannot be computed analytically by the methods covered so far. D) The length of the parametric curve   is which of the following?  A)    B)    C)    D)    E) The length integral cannot be computed analytically by the methods covered so far. E) The length integral cannot be computed analytically by the methods covered so far.

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Give the polar coordinates of the point of intersection of the lines Give the polar coordinates of the point of intersection of the lines   and   . and Give the polar coordinates of the point of intersection of the lines   and   . .

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Find the area of the shaded region in the following figure. Find the area of the shaded region in the following figure.

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The area outside The area outside   but inside   is which of the following?   A)    B)  16 C)    D)  32 E)  8 but inside The area outside   but inside   is which of the following?   A)    B)  16 C)    D)  32 E)  8 is which of the following? The area outside   but inside   is which of the following?   A)    B)  16 C)    D)  32 E)  8


A) The area outside   but inside   is which of the following?   A)    B)  16 C)    D)  32 E)  8
B) 16
C) The area outside   but inside   is which of the following?   A)    B)  16 C)    D)  32 E)  8
D) 32
E) 8

F) D) and E)
G) B) and E)

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Find the arc length of the curve given by the parametric equations Find the arc length of the curve given by the parametric equations

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