let f(x)=(x/(√(1+x^2 ))) +cos(πx) 1) prove that f(x)=0 have a solurion α inside ]0,1[ 2) use newton method to find a approximate value of α .


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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

$f (0) = 1 > 0, f (1) = \frac{1}{\sqrt{2}} - 1 < 0$ $\Rightarrow f (0) f (1) < 0 \Rightarrow f h a s a t l e a s t o n e$ $s l u t i o n i n [0, 1]$
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