### Assignment #2

**Due: 13 October, 1998**

#### Problems

**1.** Suppose that, for t > 0, we let x(t) = (1/t)cos(t) and y(t) = (1/t)sin(t).
**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

Maintained by Stefan Bilaniuk. Last updated 1999.12.03.