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Question Number 134753 by mathocean1 last updated on 06/Mar/21

f i s d e f i n e d i n [0; + \infty [.

{\begin{cases} f (0) = l n 2 \end{cases} f (x) = \int_{x}^{2 x} \frac{e^{- t}}{t} d t f o r x > 0

1) G i v e n 0 ⩽ f (x ⩽ \frac{e^{- x} - e^{- 2 x}}{x} .

C a l c u l e t h e l i m f (x) a t 0 a n d + \infty .

2) C a l c u l a t e f^{'} (x), g i v e i t s v a r i a t i o n

a n d p l o t i t s c u r v e .