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

$$\underset{x\to 0}{\lim }\frac{\sec \left({\sin }^{-1}(1-x)\right)}{3\sqrt{x}}=?$$

Answered by bobhans last updated on 28/Sep/20

$$\underset{x\to 0}{\lim }\frac{\sec \left({\sin }^{-1}(1-x)\right)}{3\sqrt{x}}=?$$$$remaining\sec \left({\sin }^{-1}(1-x)\right)=\sqrt{2x-x^2}$$$$sothelimitcanwriteas$$$$\underset{x\to 0}{\lim }\frac{\sqrt{2x-x^2}}{3\sqrt{x}}=\underset{x\to 0}{\lim }\frac{\sqrt{x}.\sqrt{2-x}}{3\sqrt{x}}=\frac{\sqrt{2}}{3}$$

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