What is the limit as x approaches 2 of arcsin(x/2) ?

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

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limit as x approaches 2 of arcsin(x/2)

x \to 2 lim (arcsin (\frac{x}{2}))

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

x \to 2 lim (arcsin (\frac{x}{2}))

Plug in the value

x = 2

= arcsin (\frac{2}{2})

Simplify

arcsin (\frac{2}{2}) : \frac{π}{2}

= \frac{π}{2}

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