let-f-x-n-1-1-n-1-ln-nx-1-give-D-f-and-study-f-on-1-2-study-the-continjity-of-f-and-calculate-lim-x-1-f-x-and-lim-x-f-x-3-prove-that-f-is-C-1-on-1-

Question Number 36748 by prof Abdo imad last updated on 05/Jun/18

l e t f (x) = \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n - 1}}{l n (n x)}

1) g i v e D_{f} a n d s t u d y f o n] 1, + \infty [

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

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

3) p r o v e t h a t f i s C^{1} o n] 1, + \infty [.