infi2HW02 - x 3. R 1 x 700 (1-x ) 300-x 300 (1-x ) 700 dx...

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2 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2007 xanaepl 18 :dybd jix`z A 4 lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz sca jxev oi` .oeilib xtqne ,f"z ,zeny xexiaa oiivl `p .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry : 1 libxz y gipp . 0 = x 0 < x 1 < x 2 < ... < x n = b : [0 ,b ] rhwd ly zniieqn dwelg P `dz .1 -iwzny egiked . λ ( P ) = max 1 <i n { x i - x i - 1 } onqp . c i [ x i - 1 ,x i ] :y jk zecewp c 1 ,c 2 ,...,c n :mi . n X i =1 ( x i - x i - 1 ) c i - b 2 2 1 2 n X i =1 ( x i - x i - 1 ) 2 b 2 λ ( P ) . b 2 = n i =1 ( x 2 i - x 2 i - 1 ) :fnx . b 2 / 2 `ed ekxre miiw R b 0 xdx y dxcbdd itl egikede mcew sirqa exfrd .2 : 2 libxz :mi`ad milxbhpi`d z` eayg 1. R 2 e 1 | log x - 1 | dx 2. R 2 0 dx 1+
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Unformatted text preview: x 3. R 1 x 700 (1-x ) 300-x 300 (1-x ) 700 dx 4. R 1-1 max { e x ,e-x } dx 5. R π cos 2 x sin 3 xdx 6. R 1-1 x 100 sin 101 xdx 7. Z 5 4 √ x 2-9 x 7 dx 8. R-3-10 √ 1 + e 2 x dx 9. R π 2 / 2 π 2 / 4 sin( √ x ) dx 10. R π-π e x 100 sin( x 99 ) dx 11. Z 2 π/ 2 2cos( x ) + sin( x ) 1 + sin( x )-cos( x ) dx 12. Z 4 2 √ x 2 + 4 x 2 dx : 3 libxz .onix inekq i"r zepezpd zexcqd ly leabd z` eayg ∑ 4 n k =2 n 1 k .1 log n q (2 n )! n !-log n .2 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 Winter '08 term at Technion.

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