aptitude

aptitude - UCSD ECE153 Prof. Young-Han Kim Handout #4...

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Unformatted text preview: UCSD ECE153 Prof. Young-Han Kim Handout #4 Tuesday, March 29, 2011 ECE153 Aptitude Test Name (Optional): Simplify the following equations as much as you can. Throughout r ∈ (0, 1). ∞ rn = 1. n=0 ∞ nrn = 2. n=0 ∞ 3. n=0 rn = n! 1 n nk r (1 − r)n−k = k 4. k=0 n 5. k k=0 ∞ 6. n=1 ∞ 7. n=1 nk r (1 − r)n−k = k 1 = n 1 = n2 2 1 1 − |x| dx = 8. −1 ∞ e−x dx = 9. 0 ∞ xe−x dx = 10. 0 ∞ ∞ e−y dydx = 11. 0 x 3 ∞ 2 e−x dx = 12. −∞ ∞ 2 xe−x dx = 13. −∞ 14. 1r r1 −1 = 15. lim x ln x = x→0 4 ...
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