lim-x-0-sec-sin-1-1-x-3-x-

Question Number 115167 by bemath last updated on 28/Sep/20

\lim_{x \to 0} \frac{\sec (\sin^{- 1} (1 - x))}{3 \sqrt{x}} = ?

Answered by bobhans last updated on 28/Sep/20

\lim_{x \to 0} \frac{\sec (\sin^{- 1} (1 - x))}{3 \sqrt{x}} = ?

r e m a i n i n g \sec (\sin^{- 1} (1 - x)) = \sqrt{2 x - x^{2}}

s o t h e l i m i t c a n w r i t e a s

\lim_{x \to 0} \frac{\sqrt{2 x - x^{2}}}{3 \sqrt{x}} = \lim_{x \to 0} \frac{\sqrt{x} . \sqrt{2 - x}}{3 \sqrt{x}} = \frac{\sqrt{2}}{3}

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