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 tangent at point E(0,f(0))


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

$l e t f_{n} (x) = {(\sqrt{1 + x^{2}} - x)}^{n} w i t h n i n t e g r n a t u r a l$ $1) f i n d \int f_{n} (x) d x$ $2) c a l c u l a t e f_{n}^{- 1} (x)$ $3) f i n d {l i m}_{x \to + \infty} f_{n} (x)$ $4) c a l c u l a t e f_{n}^{^{'}} (x) a n d f_{n}^{^{'}} (0)$ $5) g i v e t h e e q u a t i o n o f t a n g e n t a t p o i n t E (0, f (0))$
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