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Final Exam
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70 Which of the following pairs of graphs have identical asymptotes in the Cartesian xy plane (a) The graphs of y = log10 x and y = tan x (b) The graphs of y = log10 x and y = ln x (c) The graphs of y = ln x and x2 y2 = 1 (d) The graphs of y = ln x and y = csc x (e) The graphs of x2 y2 = 1 and x2 + y2 = 1 71 Consider the relation in the Cartesian xy plane represented by 9(x 2)2 + 4(y + 3)2 = 36 The graph of this relation intersects the y axis at (a) no points (b) one point (c) two points (d) four points (e) infinitely many points 72 Consider the function that we get when we multiply the square of the tangent by the square of the cotangent Let f (q) = tan2 q cot2 q
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Final Exam
What s the range of f (a) { p } (b) {p } (c) { 1} (d) {1} (e) {0} 73 Which of the following statements is true of all conic sections (a) For a circle, the eccentricity is 0; for an ellipse, the eccentricity is positive but less than 1; for a parabola, the eccentricity is equal to 1; for a hyperbola, the eccentricity is greater than 1 (b) For a parabola, the eccentricity is 0; for an ellipse, the eccentricity is positive but less than 1; for a circle, the eccentricity is equal to 1; for a hyperbola, the eccentricity is greater than 1 (c) For a hyperbola, the eccentricity is 0; for a parabola, the eccentricity is positive but less than 1; for an ellipse, the eccentricity is equal to 1; for a circle, the eccentricity is greater than 1 (d) For an ellipse, the eccentricity is 0; for a parabola, the eccentricity is positive but less than 1; for a circle, the eccentricity is equal to 1; for a hyperbola, the eccentricity is greater than 1 (e) For an ellipse, the eccentricity is 0; for a hyperbola, the eccentricity is positive but less than 1; for a circle, the eccentricity is equal to 1; for a parabola, the eccentricity is greater than 1 74 Which of the following functions appears as a straight line in log-log coordinates, meaning that both axes are graduated according to the common logarithm of the displacement (a) y = 3 (b) y = ln x (c) y = e x (d) y = log10 x (e) y = 10x 75 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-12 (a) x = t 3 and y = t 4 (b) x = t + 3 and y = t + 4 (c) x = 3t /4 and y = 4t /3 (d) x = t and y = 3t /4 (e) x = 3t and y = 4t 76 Consider the following pair of parametric equations: x = 3 cos t
Final Exam
y 6 4 (0, 0) 2 (3, 4) x 6 4 2 2 4 6 2 4 6
Figure FE-12 and
Illustration for Question 75
y = 4 sin t In the Cartesian xy plane, the graph of this system appears as (a) an ellipse centered at the origin (b) an ellipse passing through the origin (c) a hyperbola centered at the origin (d) a hyperbola passing through the origin (e) a parabola whose focus is at the origin 77 The peak-to-peak amplitude of the wave representing the function y = sin p x is (a) 2p (b) p /2 (c) 2 (d) 1/2 (e) impossible to determine without more information 78 If we divide a function by another function, the resultant function is undefined for any value of the independent variable where (a) the value of the numerator function is negative (b) the value of the denominator function is equal to 0
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