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### mt3p

Course: MATH 152, Fall 2009
School: Illinois Tech
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Word Count: 172

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152: Math Midterm 3 Fall '03 Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. (20 points) For the curve x = et - t, y = 4et/2 , 0 t 1, (a) find an equation for the tangent line to the curve at the point when t = 0; (b) find the length of the curve. 2. (20 points) (a) Find the Cartesian coordinates of the point (2, -3/4) given in polar coordinates. (b) Find a Cartesian...

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152: Math Midterm 3 Fall '03 Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. (20 points) For the curve x = et - t, y = 4et/2 , 0 t 1, (a) find an equation for the tangent line to the curve at the point when t = 0; (b) find the length of the curve. 2. (20 points) (a) Find the Cartesian coordinates of the point (2, -3/4) given in polar coordinates. (b) Find a Cartesian equation for the curve r = 3 cos given in polar equation. 3. (20 points) Find the limit of the following sequences as n . ln(n2 ) } n 2n + (-1)n sin(n) (b) { } n (a) { 4. points) (20 Find the area of the region that lies outside r = 2 - cos and inside r = 3 cos . 2 1 3 2 1 1 1 2 3 2 5. (20 points) (a) Find if the infinite series n=1 1 converge or diverge. Explain why. (Hint: you can n ln n use integral test.) (b) Find if the infinite series (-1)n ln n converge absolutely, converge conditionally or n...

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