find-the-real-root-of-x-x-3-3-x-5-10-x-7-42-x-9-216-x-11-1320-443-please-if-any-simple-expansion-of-it-then-plz-tell-me-

Question Number 50551 by pooja24 last updated on 17/Dec/18

f i n d t h e r e a l r o o t o f

x - \frac{x^{3}}{3} + \frac{x^{5}}{10} - \frac{x^{7}}{42} + \frac{x^{9}}{216} - \frac{x^{11}}{1320} + \dots \dots = . 443

p l e a s e i f a n y s i m p l e e x p a n s i o n o f i t

t h e n p l z t e l l m e

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Dec/18

f (x) = x - \frac{x^{3}}{3} + \frac{x^{5}}{10} - \frac{x^{7}}{42} + \frac{x^{9}}{216} - \frac{x^{11}}{1320} + \dots

\frac{d f (x)}{d x} = 1 - x^{2} + \frac{x^{4}}{2} - \frac{x^{6}}{6} + \frac{x^{8}}{24} - \frac{x^{10}}{120} + \dots

l e t = k = x^{2}

R i g h t h a n d s i d e

1 - k + \frac{k^{2}}{2!} - \frac{k^{3}}{3!} + \frac{k^{4}}{4!} - \frac{k^{5}}{5!} + \dots

= e^{- k}

= e^{- x^{2}}

s o \frac{d f (x)}{d x} = e^{- x^{2}}

f (x) = \int e^{- x^{2}} d x

[f r o m t a b l e e^{- 0.812} \approx 0.443