
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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PLease solve both a and b

Transcribed Image Text:(1) Suppose that (an)neN is a sequence of positive numbers that converges to a positive
real number a.
(a) Show that there exists an M such that an > for all n > M.
(b) Prove that lim loge (an) = loge (a) using the definition of convergence. (You may
use the inequality | loge (x) - loge (y)| ≤
for
|x-y
min{x,y} x, y > 0.)
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