Calculus Challenge 2001
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1. Evaluate the integral 1
dx
x
1+ 3
0
2. Show that xe ex for all positive real numbers x and determine all
number x for which equality holds.
3. Let > ?1 and > ?1. Calculate limn!1 n?
4. Find the sum of the following series: P1
n
=1
+n
+n
1 +2 +
1 +2 +
ln(2n )
en
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5. Find the antiderivative: pedx
a ?ex
?
6. Does the series P1
n ne
=1
pn
converge or diverge? Justify your answer.