MTH 162 Midterm: MTH 162 University of Rochester Fall 10Exam2 Solutions
31 Jan 2019
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2 (1 + x) 1 + 1 dx + 2 z 1 (1 x) 1 + 1 dx. Consider the parametric curve x = cos(t), y = sin(2t), t [0, 2 ]. (a) at what points is the tangent horizontal or vertical? (b) the curve passes through the origin twice. What are the slopes of the two tangent lines to the curve at the origin? (c) find the equation of the form y = mx + b for the tangent at t = . The tangent line is horizontal when this derivative is 0, namely when t = The tangent line is vertical when the derivative is unde ned, namely at t = 0 and t = . The corresponding two cartesian points are ( 1, 0). Solution: (b) the curve passes through the origin at t = . Solution: (c) at t = /6 we have x = y = tangent line is.
