Practice Exam 3 - PRACTICEEXAM#3 Math185,Chapters10&11...

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PRACTICE EXAM #3 Math 185, Chapters 10 & 11 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Parametric equations and and a parameter interval for the motion of a particle in the xy - plane are given. Identify the particle ʹ s path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. 1) x = 9t 2 , y = 3t, - ∞ ≤ t ≤ ∞ x -5 -4 -3 -2 -1 1 2 3 4 5 y 5 4 3 2 1 -1 -2 -3 -4 -5 1) 2) x = 2t + 3, y = 6t + 6, - ∞ ≤ t ≤ ∞ x -5 -4 -3 -2 -1 1 2 3 4 5 y 5 4 3 2 1 -1 -2 -3 -4 -5 2) 1
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Find an equation for the line tangent to the curve at the point defined by the given value of t. 3) x = t + cos t, y = 2 - sin t, t = π 6 3) 4) x = 8t 2 - 5, y = t 3 , t = 1 4) Find the value of d 2 y/dx 2 at the point defined by the given value of t. 5) x = t + 3 , y = - t, t = 22 5) Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the curve x = f(t), y = g(t)at the given value of t. 6) 2x + 4x 3/2 = t 3 + t, y(t + 1) - 4t y = 9, t = 0 6) 7) x = t sin t + t, y cos t + y = 2t, t = π 2 7) 2
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Find the length of the curve.
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