What is the limit as x approaches 1/2 of arccos(x) ?

The limit as x approaches 1/2 of arccos(x) is pi/3

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limit as x approaches 1/2 of arccos(x)

x \to \frac{1}{2} lim (arccos (x))

\frac{π}{3}

Decimal Notation

1.04719 \dots

Solution steps

x \to \frac{1}{2} lim (arccos (x))

Plug in the value

x = \frac{1}{2}

= arccos (\frac{1}{2})

Use the following trivial identity:

arccos (\frac{1}{2}) = \frac{π}{3}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{3}

x \to 1 - lim (1 + x^{3})

x \to 3 lim (\frac{x}{ln ( x - 2 )})

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

x \to 0 lim (2 arctan (x))

x \to 0 + lim (\frac{( x cos ( x ) )}{2 x})

What is the limit as x approaches 1/2 of arccos(x) ?
The limit as x approaches 1/2 of arccos(x) is pi/3