What is the limit as x approaches 0 of x/(arcsin(x)) ?

The limit as x approaches 0 of x/(arcsin(x)) is 1

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limit as x approaches 0 of x/(arcsin(x))

x \to 0 lim (\frac{x}{arcsin ( x )})

1

Solution steps

x \to 0 lim (\frac{x}{arcsin ( x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{\frac{1}{1 - x ^{2}}})

Plug in the value

x = 0

= \frac{1}{\frac{1}{1 - 0 ^{2}}}

Simplify

\frac{1}{\frac{1}{1 - 0 ^{2}}} : 1

= 1

What is the limit as x approaches 0 of x/(arcsin(x)) ?
The limit as x approaches 0 of x/(arcsin(x)) is 1