Infi2_hw4 - 4 oeilib-2007 aia`(104281 2 itpi` 14...

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Unformatted text preview: 4 oeilib -2007 aia` - (104281) 2 itpi` 14 : 00 ,17.6.2007 ,oey`x mei :dybd jix`z :qpkzn mi`ad milxbhpi`d oian in reawl .1 1 . 0 . tan(x)dx x + sin(x2 ) dx x2 - 2x . 0 (`) (a) 2 . (1 - e- x )dx 1 (b) 2 e-x x9 dx (c) - 2 zniiwn xnelk ,oniqd ziivwpet `id .( sign(x) xy`k) sign(sin(x)) dx - xear (d) sign(0) = 0 ,x < 0 1 xear sign(x) = -1 ,x > 0 sign(x) = 1 .2 ?xcazn ?hlgda qpkzn ?qpkzn sin(x )dx lxbhpi`d xhnxtd ly mikxr eli` xear miieqn iynn xtqn .zcxei zipehepene zilily i` f : [a, ) R `dze .limx xf (x) = 0 y egiked .qpkzn ziliaxbhpi` a a a `di .3 f (x)dx lxbhpi`dy gipp `di .4 f : [a, ) R y gipp .miieqn iynn xtqn -xbhpi` zxfbpdy ,dxifb . f sqepa m`y egiked .qpkzn f (x)dx lxbhpi`dy oke limx f (x) = 0 f` ,qpkzn a f (x)dx lxbhpi`dy oke zilia . a 1 p>0 xefgn mr zixefgne ziliaxbhpi` f (x) dx x f :RR `dz .5 lxbhpi`dy jkl witqne igxkd i`pzy egiked , . 0<1 ozpida p 0 f (x)dx = 0 y `ed qpkzi 1 ...
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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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