hw 02 solution

X x2 a2 x a fx a fa h1 a h1 x x a x a fx h2 x x a x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: b x x b a x a x b b x fa x a a x bfx x fb h if g has only simple roots the results from f generalizes in a straighforward manner xi f xi fx gx x fx hi x x xi x hi xi xi i i but g ' xi hi x x xi ' x xi hi xi 1 PROBLEM 4 Let' s take any test function f x and evaluate a lim a 0 fx exp a a x2 a2 x f ay exp y2 y by changing the variable of integration y lim f a y 0 x a y2 y f0 lim exp y2 0 a y f0 exp because exp y2 y prove it b lim g fx sin g x x g x f y g sin y y y by changing the variable of integration y lim f y g sin y y y f0 sin y y gx y f0 lim g because sin y y y show that by using a complex contour integral c lim 0 fx 2 x2 f x y 1 1 y2 y by changing the variable of integration y lim f 0 x 1 1 y2 y f0 lim 0 y 1 1 y2 y f0 because 1 1 y2 y arctan arctan 2 2...
View Full Document

Ask a homework question - tutors are online