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

The limit as x approaches 3 of arcsin(x/3) is pi/2

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

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

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

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

Plug in the value

x = 3

= arcsin (\frac{3}{3})

Simplify

arcsin (\frac{3}{3}) : \frac{π}{2}

= \frac{π}{2}

x \to 2 lim (- 2 x)

x \to 2 + lim (\frac{1 - x}{2 - x})

x \to - 6 lim (\frac{x ^{2}}{∣ x ∣})

x \to 0 lim (3 - 3 x + 7 x^{2})

x \to 0 - lim (x (1 - x)^{\frac{1}{x}})

What is the limit as x approaches 3 of arcsin(x/3) ?
The limit as x approaches 3 of arcsin(x/3) is pi/2