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(c) the value of the denominator function is negative (d) the values of both the numerator and denominator function are negative (e) the values of the numerator and denominator function have opposite signs 79 Consider the following system of parametric equations in Cartesian xyz space: x=t y = 1 z = 2t 2 7t This system represents (a) a straight line in a plane parallel to the xy plane (b) a hyperbola in a plane parallel to the xy plane (c) a circle in a plane parallel to the yz plane (d) a parabola in a plane parallel to the xz plane (e) an ellipse that intersects the z axis at two points 80 What does the following expression portray S = 1/2 + 1/2 1/2 + 1/2 1/2 + 1/2 1/2 + (a) (b) (c) (d) (e) An infinite arithmetic series An infinite harmonic series An infinite geometric series An infinite hyperbolic series An infinite circular series
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81 Suppose that t is a parameter on which two variables x and y depend Which of the following pairs of parametric equations can represent the straight line graphed in Fig FE-13 (a) x = t 5 and y = t 3 (b) x = 5t and y = 3t (c) x = 3t /5 and y = 5t /3 (d) x = t and y = 3 3t /5 (e) x = 3t and y = 5t 82 Consider an object in Cartesian xyz space whose parametric equations are x = (cos t)/p y = p sin t z = pt The graph of this object is an elliptical
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y 6 4 (0, 3) 2 x 6 4 2 2 (5, 0) 4 6 2 4
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Figure FE-13
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Illustration for Question 81
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(a) (b) (c) (d) (e)
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83 In an infinite arithmetic sequence, we can find a constant that determines (a) the ratio of any term to its successor (b) the difference between any term and its successor (c) the product of any term and its successor (d) the sum of all the terms (e) the product of all the terms 84 If the ordered pair ( 1,8) represents a point that lies on the graph of a relation f in the Cartesian xy plane, then its counterpoint on the graph of the inverse relation f 1 is represented by the ordered pair (a) (1, 8) (b) ( 1,1/8) (c) (8, 1) (d) (1/8, 1) (e) ( 1/8,1)
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Final Exam
85 In the Cartesian xy plane, a unit hyperbola can be represented by which one of the following pairs of parametric equations, where t is the parameter (a) x = t 2 and y = t 2 (b) x = cos t and y = sin t (c) x = sin t and y = sin t (d) x = cos t and y = cos t (e) x = t and y = (t 2 1)1/2 86 Which of the following equations might describe the hyperboloid of two sheets shown in Fig FE-14 Assume the center of the entire object is at the origin (a) x 2/2 + y 2/2 z 2/3 = 1 (b) x 2/2 + y 2/2 + z 2/3 = 1 (c) x 2/2 + y 2/2 + z 2/3 = 0 (d) x/2 + y/2 + z/3 = 1 (e) (x 2)(y + 2)(z 3) = 1 87 If we move the entire object in Fig FE-14 to place its center at the point (5,5,5) rather than at the origin, its equation becomes which one of the following (a) x 2/2 + y 2/2 + z 2/3 = 5 (b) 5x 2/2 + 5y 2/2 + 5z 2/3 = 0
Figure FE-14
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