What is the limit as x approaches infinity of arcsin((2x)/(5+4x)) ?

The limit as x approaches infinity of arcsin((2x)/(5+4x)) is pi/6

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limit as x approaches infinity of arcsin((2x)/(5+4x))

x \to \infty lim (arcsin (\frac{2 x}{5 + 4 x}))

\frac{π}{6}

Decimal Notation

0.52359 \dots

Solution steps

x \to \infty lim (arcsin (\frac{2 x}{5 + 4 x}))

Apply the Limit Chain Rule:

\frac{π}{6}

= \frac{π}{6}

\frac{\partial}{\partial x} (e^{4 x y} \cdot 4 y)

x^{2} y^{^{'}} + 2 x y = 5 y^{3}

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0

y^{^{'}} = \frac{( x ^{2} + y )}{x + 1}

y^{^{'}} + \frac{y}{x} = x^{- 4}

What is the limit as x approaches infinity of arcsin((2x)/(5+4x)) ?
The limit as x approaches infinity of arcsin((2x)/(5+4x)) is pi/6