find-a-equivalent-to-f-x-cos-sinx-for-x-v-0-2-find-a-equivalent-to-g-x-tan-pi-2x-1-x-0-

Question Number 40091 by maxmathsup by imad last updated on 15/Jul/18

f i n d a e q u i v a l e n t t o f (x) = c o s (s i n x) f o r x \in v (0)

2) f i n d a e q u i v a l e n t t o g (x) = t a n (\frac{π}{2 x + 1}) (x \to 0)

Commented by math khazana by abdo last updated on 26/Jul/18

1) w e h a v e s i n x \sim x \Rightarrow c o s (s i n x) \sim c o s x \sim 1 - \frac{x^{2}}{2}

\Rightarrow f (x) \sim 1 - \frac{x^{2}}{2} (x \to 0)

2) w e h a v e \frac{π}{2 x + 1} = \frac{π}{1 + 2 x} \sim π (1 - 2 x) \Rightarrow

t a n (\frac{π}{2 x + 1}) \sim t a n (π (1 - 2 x)) \sim - t a n (2 π x) \sim - 2 π x \Rightarrow

g (x) \sim - 2 π x (x \to 0)