fall17mth143.practice2.9-ParametricCalc.pdf

# Use upper case inf for positive infinity and upper

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Use upper-case ”INF” for positive infinity and upper-case ”NINF” for negative infinity. If the curve is never concave up- ward, type an upper-case ”N” in the answer field. t -interval: < t < Answer(s) submitted: (incorrect) Correct Answers: 3*(2*t/(3*tˆ2-12)) 3*(-2*(tˆ2+4)/(9*(tˆ2-4)ˆ3)) -2 2 5. (1 point) (a) Find dy dx expressed as a function of t for the given the parametric equations: x = cos 7 ( t ) y = 3sin 2 ( t ) dy dx = . (b) Find d 2 y dx 2 expressed as a function of t. d 2 y dx 2 = . (c) Except for at the points where dy dx is undefined, is the curve concave up or concave down? (Enter ’up’ or ’down’). Concave . Answer(s) submitted: (incorrect) Correct Answers: 1

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(-2*3/7)*(1/(cos(t)**(7-2))) (2*3*(7-2)/(7*7))*(1/(cos(t)**(2*7-2))) up 6. (1 point) Consider the curve given by the parametric equa- tions x = t ( t 2 - 3 ) , y = 8 ( t 2 - 3 ) a.) Determine the point on the curve where the tangent is horizontal. t = b.) Determine the points t 1 , t 2 where the tangent is vertical and t 1 < t 2 . t 1 = t 2 = Answer(s) submitted: (incorrect) Correct Answers: 0 -1 1 7. (1 point) You are given the parametric equations x = te t , y = te - t . (a) Use calculus to find the Cartesian coordinates of the high- est point on the parametric curve.
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