let-f-n-x-1-x-2-x-n-with-n-integr-natural-1-find-f-n-x-dx-2-calculate-f-n-1-x-3-find-lim-x-f-n-x-4-calculate-f-n-x-and-f-n-0-5-give-the-equation-of

Question Number 46422 by maxmathsup by imad last updated on 25/Oct/18

l e t f_{n} (x) = {(\sqrt{1 + x^{2}} - x)}^{n} w i t h n i n t e g r n a t u r a l

1) f i n d \int f_{n} (x) d x

2) c a l c u l a t e f_{n}^{- 1} (x)

3) f i n d {l i m}_{x \to + \infty} f_{n} (x)

4) c a l c u l a t e f_{n}^{^{'}} (x) a n d f_{n}^{^{'}} (0)

5) g i v e t h e e q u a t i o n o f t a n g e n t a t p o i n t E (0, f (0))