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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= 1

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