let-f-x-arctan-1-e-1-x-2-calculate-f-x-and-f-x-1-find-lim-x-f-x-and-lim-x-f-x-3-study-the-variation-of-f-x-4-give-the-equation-of-tangent-to-C-f-at-A-1-f-1-

Question Number 67015 by mathmax by abdo last updated on 21/Aug/19

l e t f (x) = a r c t a n (1 + e^{- \sqrt{1 + x^{2}}})

c a l c u l a t e f^{^{'}} (x) a n d f^{^{″}} (x) .

1) f i n d {l i m}_{x \to + \infty} f (x) a n d {l i m}_{x \to - \infty} f (x)

3) s t u d y t h e v a r i a t i o n o f f (x)

4) g i v e t h e e q u a t i o n o f t a n g e n t t o C_{f} a t A (1, f (1))