homework2 - FYMM Ib Laskuharjoitus 2 syksy 2008 Palautetaan...

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FYMM Ib Laskuharjoitus 2 syksy 2008 Palautetaan viimeistään ma 10.11. klo 12.00 1. Osoita, että a) x a = o ( x b ) , x + , a < b ; b) x a = o ( x b ) , x +0 , a > b ; c) ln x = o ( x a ) , x + , a > 0 . 2. Osoita, että x Z 0 t 2 + 1 dt = x 2 2 + 1 2 ln x + O (1) , x + . 3. Osoita, että x Z 1 e t t dt e x x , x + . 4. Osoita, että Z 0 t a - 1 e - λt dt t 2 + 1 Γ( a ) λ a , λ + ,a > 0 . 5. Osoita Laplacen menetelmää käyttäen, että π Z 0 sin n xdx r 2 π n , n → ∞ .
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FYMM Ib Exercise 2 Autumn 2008 Due to Mon 10.11. at 12.00 1. Show that a) x a = o ( x b ) , x + , a < b ; b) x a = o ( x b ) , x +0 , a > b ; c) ln x = o ( x a
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This note was uploaded on 01/23/2009 for the course THEORETICA FYMM 1B taught by Professor Juhahonkonen. during the Winter '08 term at Uni. Helsinki.

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homework2 - FYMM Ib Laskuharjoitus 2 syksy 2008 Palautetaan...

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