a. Sketch the curve defined by these parametric equations. [2]
b. Determine for which values of t the point (x(t),y(t)) is within a distance of 0.000001 from (0,0). [4]
2. To celebrate his birthday, Jacob decides to spend a day and night on the drumlin. (What he does up there is left to your imagination...) He starts up the path to his campsite at 8 a.m. on his birthday and starts back down at 8 a.m. the following morning. Show that if Jacob takes the same path coming back, then there is a spot on the path which he occupies at exactly the same time of day each way. [4]
Bonus. Show that there are two (not necessarily different) irrational numbers a and b such that a^b is rational. [1]
Department of Mathematics
Trent University