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Practice6answers

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Unformatted text preview: √ 3. Determine the angle of intersection of the paths r (t) = t2 + t + 2, sin ( 3 t) and √ s(t) = 2e 3 t , 2t as they cross at the time t = 0 through the point (2, 0). √ √ √ dx1 dy1 = 1, 3 = 2t + 1, 3 cos ( 3t) , t=0 dt dt t=0 √√ = 2 3e 3t , 2 √ = 2 3, 2 t=0 t=0 √ √ 1, 3 · 2 3, 2 √ √ angle between curves: θ = arccos | 1, 3 || 2 3, 2 | dx2 dy2 , dt dt √ 43 = arccos 2·4 = π 6 4. Determine the arc length of the path x(t) = et + e−t , y (t) = 5 − 2t on 0 ≤ t ≤ 4. 2 2 dx dy t −t 2 2t −2t = (e − e ) = e − 2 + e and =4 dt dt dx dt 2 dy + dt 2 = e2t + 2 + e−2t = (et + e−t )2 4 4 (dx...
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This note was uploaded on 05/30/2013 for the course MATH 0230 taught by Professor Athanas during the Spring '08 term at Pittsburgh.

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