Now that we have shown the existence of Euler's constant the hard way we will solve a much more general problem the easy way and watch y appear out of thin air, so to speak. Let f be continuous and decreasing on [1, () and let

Bn is the area of the shaded region in Figure 3.
(a) Why is it obvious that Bn increases with n?
(b) Show that Bn ( f(1). Simply shift all the little shaded pieces leftward into the first rectangle.

(d) How do we get ( out of this?

Transcribed Image Text:

f(x) dx lim B yfx) +1 x Figure 3