f-t-0-e-xt-x-t-2-dx-with-t-0-1-study-the-set-of-definition-for-f-t-2-study-the-continuity-of-f-3-study-the-derivability-of-f-4-developp-f-at-integr-serie-

Question Number 62808 by mathmax by abdo last updated on 25/Jun/19

f (t) = \int_{0}^{+ \infty} \frac{e^{- x t}}{{(x + t)}^{2}} d x w i t h t ⩾ 0

1) s t u d y t h e s e t o f d e f i n i t i o n f o r f (t)

2) s t u d y t h e c o n t i n u i t y o f f

3) s t u d y t h e d e r i v a b i l i t y o f f

4) d e v e l o p p f a t i n t e g r s e r i e