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PracticeTest5 - 2 4 2 3 x y if t = x-1 Simplify each...

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Practice Test #5 MAC2312 Directions: Use this practice test as a guide for your study for Test #5. This exam is not comprehensive, so study your quiz, class notes and homework problems in addition to completing this exam. Solutions are posted on the course website under “Solutions”. 1) For the parabola ) 1 ( 12 ) 3 ( 2 x y , find the vertex and focus as ordered pairs, find the equation of the directrix, and sketch. Label all information on your sketch. 2) Find the standard equation of the hyperbola given by 0 100 40 36 4 9 2 2 y x y x . 3) Sketch the plane curve given by the parametric equations 7 5 t x , 4 3 t y for 2 3 t . Use a table of values for x, y and t, and show appropriate directional arrows to indicate increasing t values. 4) For the equations given in problem #4, eliminate the parameter to find a rectangular equation where y is a function of x. Simplify completely, finding a common denominator. 5) Find a set of parametric equations that represent the graph of
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Unformatted text preview: 2 ) 4 ( 2 3 x y if t = x -1. Simplify each completely. 6) For the plane curve given by ) 3 cos( 2 x , ) 4 sin( 5 y , find the generalized slope dx dy and the specific slope when x = 0. Restrict values of your angle to the first quadrant. 7) Find the arc length of the plane curve given by cos 2 5 x , 1 sin 2 y on the interval 3 4 , 6 . 8) For the polar coordinate 6 7 , 3 , do the following: a) Graph the polar coordinate. b) Find two equivalent polar coordinates: _______ and _______ c) Find the corresponding rectangular coordinate: ____________ 9) For the rectangular coordinate 3 , 3 , find the corresponding polar coordinate. 10) Graph ) 2 sin( 5 r by filling in the chart below and plotting each point. 0 4 2 4 3 4 5 2 3 4 7 2 r 11) Find the area of one petal of ) 3 cos( 4 r . First, find the tangent lines at the pole, then find the area using those values as your limits of integration....
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