This preview shows page 1. Sign up to view the full content.
Unformatted text preview: f ( x ) = 0 if x <2 , 1 if2 < x <1 , 2 if1 < x < 1 , 3 if 1 < x < 3 , 0 if 3 < x. 17. We use the deFnition (7) of the derivative of a generalized function and the fact that the integral against a delta function a picks up the value of the function at a . Thus ( x ) , f ( x ) = ( x ) ,f ( x ) = ( x ) , f ( x ) = ( x ) 1 ( x ) , f ( x ) =f (0) + f (1) . 21. rom Exercise 7, we have ( x ) = 1 a ( U2 a ( x ) Ua ( x ) )1 a ( U a ( x ) U 2 a ( x ) ) . Using (9) (or arguing using jumps on the graph), we Fnd ( x ) = 1 a ( 2 a ( x )a ( x ) )1 a ( a ( x ) 2 a ( x ) ) = 1 a ( 2 a ( x )a ( x ) a ( x )+ 2 a ( x ) ) . 25. Using the deFnition of and the deFnition of a derivative of a generalized...
View Full
Document
 Fall '11
 StuartChalk

Click to edit the document details