infi2HW2

infi2HW2 - 2 A4'qn milibxz oeilb 104281 23 2 itpi`.mixdva...

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Unformatted text preview: 2 A4 'qn milibxz oeilb - 104281 23 - 2 itpi` .mixdva 12 : 00 dry cr -- 2006 lixt`l :dybd jix`z lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz z`e cinlzd my z` xexiaa oiivl `p .micigia dybdd .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry sca jxev oi` .f"z xtqn : 1 libxz :miiwzn a>0 lkl m"m` zibef i` a f (x) :egiked .dtivx divwpet f (x) idz f (x)dx = 0 -a : 2 libxz :mi`ad milxbhpi`d z` eayg 2e 1 | log x - 1|dx .1 2 dx .2 0 1+ x 1 0 x700 (1 - x)300 - x300 (1 - x)700 dx 1 -1 .3 .4 .5 .6 max{ex , e-x }dx 0 cos2 x sin3 xdx x100 sin101 xdx : 1 -1 3 libxz .zepezpd zexcqd ly leabd z` eayg an = bn = 1 9n2 -1 1 n2 + 2 n2 + + n-1 .1 n2 + 1 9n2 -4 1 (n+2)2 + + + + 1 .2 9n2 -n2 cn = n 1 (n+1)2 + 1 (n+n)2 .3 1 : 4 libxz :mi`ad zeleabd z` eayg .1 x0 lim x -t2 e dt 0 sin x t cos tdt 0 x0 lim x2 0 .2 arctan(t)dt x 2 t dt 0 : 5 libxz x log 2 dt = t-1 6 e :d`eeynd z` exzt : 6 libxz dwelg dxear zniiwy divwpet `id ef [a, b] rhwa zebxcn zivwpet a = x0 < x1 < < xn = b :egiked .i :y jk = 1, 2, . . . , n xear (xi-1 , xi ) rhw zz lka dreaw - a ziliaxbhpi` f (x) - y jk (x) zebxcn zivwpet zniiw b >0 b lkl if` [a, b] f (x) m` .1 f (x)dx - a a (x)dx < .x [a, b] lkl (x) f (x) :miiwzne :egiked .ziliaxbhpi` divwpet 2 n f (x) idz .2 lim f (x) cos(nx)dx = 0 0 .zebxcn zivwpet xear ziy`x egiked :fnx : 7 libxz :egiked .[a, b] - a x lkl f (x) > 0 ,xnelk .[a, b] rhwa ziaeige ziliaxbhpi` divwpet f (x) idz b . f (x)dx > 0 a 2 ...
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This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Spring '08 term at Technion.

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infi2HW2 - 2 A4'qn milibxz oeilb 104281 23 2 itpi`.mixdva...

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