lim-x-0-arcsin-x-2-x-2-x-4-tan-2-x-

Question Number 101075 by bemath last updated on 30/Jun/20

\lim_{x \to 0} \frac{\arcsin (x^{2}) - x^{2}}{x^{4} \tan^{2} x} = ?

Commented by Dwaipayan Shikari last updated on 30/Jun/20

\lim_{x \to 0} \frac{x^{2} + \frac{x^{6}}{6} - x^{2}}{x^{4} . x^{2}} = \frac{\frac{x^{6}}{6}}{x^{6}} = \frac{1}{6}

{A s x \to 0 s u p p o s e t a n x = x {t a n}^{2} x = x^{2}} {A n d m a c l a u r i n s e r i e s f o r \sin^{- 1} x^{2}}