Practice Final 2 - PRACTICEFINAL#2 Math185,Chapters10&11...

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PRACTICE FINAL #2 Math 185, Chapters 10 & 11 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) Find an equation for the line tangent to the curve at the point defined by the given value of t. 2) x = 8t 2 - 5, y = t 3 , t = 1 2) 1
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Find the value of d 2 y/dx 2 at the point defined by the given value of t. 3) x = t + 3 , y = - t, t = 22 3) 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. 4) 2x + 4x 3/2 = t 3 + t, y(t + 1) - 4t y = 9, t = 0 4) Find the length of the curve. 5) x = t 3 , y = 2t 2 , 0 t 1 5) Find the area of the surface generated by revolving the curves about the indicated axis. 6) x = sin t, y = 8 + cos t, 0 t 2 π ; x - axis 6) 2
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Describe the graph of the polar equation. 7) r 2 = 48r cos θ 7) Replace the polar equation with an equivalent Cartesian equation.
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