What is the limit as x approaches 0 of (arcsin(3x))/(arctan(5x)) ?

The limit as x approaches 0 of (arcsin(3x))/(arctan(5x)) is 3/5

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limit as x approaches 0 of (arcsin(3x))/(arctan(5x))

x \to 0 lim (\frac{arcsin ( 3 x )}{arctan ( 5 x )})

\frac{3}{5}

Decimal

0.6

Solution steps

x \to 0 lim (\frac{arcsin ( 3 x )}{arctan ( 5 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{\frac{3}{1 - 9 x ^{2}}}{\frac{5}{25 x ^{2} + 1}})

Plug in the value

x = 0

= \frac{\frac{3}{1 - 9 \cdot 0 ^{2}}}{\frac{5}{25 \cdot 0 ^{2} + 1}}

Simplify

\frac{\frac{3}{1 - 9 \cdot 0 ^{2}}}{\frac{5}{25 \cdot 0 ^{2} + 1}} : \frac{3}{5}

= \frac{3}{5}

What is the limit as x approaches 0 of (arcsin(3x))/(arctan(5x)) ?
The limit as x approaches 0 of (arcsin(3x))/(arctan(5x)) is 3/5