What is the limit as x approaches 0 of (arcsin(3x))/x ?

The limit as x approaches 0 of (arcsin(3x))/x is 3

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limit as x approaches 0 of (arcsin(3x))/x

x \to 0 lim (\frac{arcsin ( 3 x )}{x})

3

Solution steps

x \to 0 lim (\frac{arcsin ( 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{\frac{3}{1 - 9 x ^{2}}}{1})

= x \to 0 lim (\frac{\frac{3}{1 - 9 x ^{2}}}{1})

Plug in the value

x = 0

= \frac{\frac{3}{1 - 9 \cdot 0 ^{2}}}{1}

Simplify

\frac{\frac{3}{1 - 9 \cdot 0 ^{2}}}{1} : 3

= 3

x^{\frac{1}{2}} (2 x^{\frac{1}{2}} - 1)

- \frac{1}{5} x^{2} - \frac{6}{5} x + \frac{7}{5}, [- 5, 5]

y^{^{'}} = 24.5 - \frac{7 y}{( 280 - 2 x )}

\int \frac{1}{x} + 2 d x

\int \frac{x ^{3}}{9 x ^{2} + 7} d x

What is the limit as x approaches 0 of (arcsin(3x))/x ?
The limit as x approaches 0 of (arcsin(3x))/x is 3