MathDB

803

Part of 2012 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 803

Source: 2012 Yokohama National University /Science, 2nd exam # 1

3/13/2012
Answer the following questions:
(1) Evaluate ∫−11(1−x2)e−2xdx.\int_{-1}^1 (1-x^2)e^{-2x}dx.
(2) Find lim⁡n→∞{(2n)!n!nn}1n.\lim_{n\to\infty} \left\{\frac{(2n)!}{n!n^n}\right\}^{\frac{1}{n}}.
calculusintegrationlimitlogarithmsfactorialcalculus computations