let-f-x-x-1-x-2-cos-pix-1-prove-that-f-x-0-have-a-solurion-inside-0-1-2-use-newton-method-to-find-a-approximate-value-of-

Question Number 57406 by Abdo msup. last updated on 03/Apr/19

l e t f (x) = \frac{x}{\sqrt{1 + x^{2}}} + c o s (π x)

1) p r o v e t h a t f (x) = 0 h a v e a s o l u r i o n α i n s i d e] 0, 1 [

2) u s e n e w t o n m e t h o d t o f i n d a a p p r o x i m a t e

v a l u e o f α .

Commented by kaivan.ahmadi last updated on 04/Apr/19

f (0) = 1 > 0, f (1) = \frac{1}{\sqrt{2}} - 1 < 0

\Rightarrow f (0) f (1) < 0 \Rightarrow f h a s a t l e a s t o n e

s l u t i o n i n [0, 1]