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MA 22S1 Assignment 1 Due 12-14 October 2015 Id: 22S1-f2015-1.m4,v 1.3 2015/10/11 19:11:54 john Exp john 1. Convert x = 2t + 3, y = 4t + 5 from paramatric to implicit form and x + 2y = 3 from implicit to parametric. 2. Find the tangent lines to the parametric curve x= 1 + t2 , 1 − t2 2t 1 − t2 at the points corresponding to the parameter values t = 0, t = 2 and t = −3. 3. Find the length of the parametric curve x= 1 + t2 , 1 − t2 y= 2t , 1 − t2 1 1 − <t< . 2 2 Note: the integral you get is not one with elementary indefinite integral, so you can’t get a closed form solution. So just simplify the integrand as much as you can, and leave it unintegrated, as in the last arc length example I did in lecture. 1 Id: 22S1-f2015-1.m4,v 1.3 2015/10/11 19:11:54 john Exp john 2 4. Convert r 4 sin2 (2θ) = 4 from polar to Cartesian coordinates and 1 1 y = x2 − 2 2 from Cartesian to polar coordinates.