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quiz1.2011.sol (1) - Name Master solution Matric 007 Date...

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Unformatted text preview: Name: Master solution Matric: 007 Date: 28 September 2011 QUIZ 1 Solution: a. Even component: Odd component: ( ) = 0. 5 ( ( ) + ( − ) ) ( ) = 0. 5 ( ) − (− ) b. ( ) = ( − 1) − ( − 3) − 2 ( − 5) c. = ∫ | ( )| = ∫ | − 1| ( = = = 3 + ∫ |2 | − 2 + 1) − + + + 4 ∙ ( 5 − 3) − 9 + 3 − ( − 1 + 1) + 4 ∙ 2 Bonus point: d. ( )= 4 0, <1 −1 1≤ ≤3 2, 3≤ ≤5 0, >5 = 10 ⎧ ⎪ ⎪ ( )= () = ⎨ ⎪ ⎪ ⎩ 0, <1 ( − 1) , ( − 1) + ( − 1) 1≤ ≤3 2 + , 2 3≤ ≤5 , >5 0, <1 ( ) = 0.5 − + 0.5, 1 ≤ ≤ 3 2 − 4, 3≤ ≤5 6, >5 Fig. 2: The integral ( ) = ∫ () 2 ...
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