Really Fun Limit Problem

Here’s a great problem that a student brought to me today. For those who’ve been wanting a ‘problem of the month,’ here you go:

The figure shows a fixed circle C_1 with equation \left(x-1\right)^2+y^2=1 and a shrinking circle C_2 with radius r and center the origin (in red). P is the point (0,r), Q is the upper point of intersection of the two circles, and R is the point of intersection of the line PQ and the x-axis. What happens to R as C_2 shrinks, that is, as r\rightarrow 0^{+}

Advertisements

2 thoughts on “Really Fun Limit Problem

  1. Pingback: Really Interesting Limit Problem (again) « Random Walks

  2. Pingback: Really Fun Limit Problem (revisited) « Random Walks

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s