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

The limit as x approaches 0 of arcsin(e^x) is pi/2

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limit as x approaches 0 of arcsin(e^x)

x \to 0 lim (arcsin (e^{x}))

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

x \to 0 lim (arcsin (e^{x}))

Plug in the value

x = 0

= arcsin (e^{0})

Simplify

arcsin (e^{0}) : \frac{π}{2}

= \frac{π}{2}

\frac{d}{d x} (\frac{( x - 1 )}{x + 1})

\frac{d}{d x} (\frac{5 x ^{4}}{2 - x ^{2}})

x \to \infty lim (\frac{x ^{2} - 9}{2 x - 6})

y^{^{'}} - y tan (x) = cos (x)

\frac{\partial}{\partial s} (sin (s + t))

What is the limit as x approaches 0 of arcsin(e^x) ?
The limit as x approaches 0 of arcsin(e^x) is pi/2