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Calculus Challenge 2001 R 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 R 5. Find the antiderivative: pedx a ?ex ? 6. Does the series P1 n ne =1 pn converge or diverge? Justify your answer.