What is the limit as x approaches pi/3 of ((sin(x)-(sqrt(3))/2))/(x-pi/3) ?

The limit as x approaches pi/3 of ((sin(x)-(sqrt(3))/2))/(x-pi/3) is 1/2

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limit as x approaches pi/3 of ((sin(x)-(sqrt(3))/2))/(x-pi/3)

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Apply L'Hopital's Rule

: x \to \frac{π}{3} lim (\frac{cos ( x )}{1})

= x \to \frac{π}{3} lim (\frac{cos ( x )}{1})

Plug in the value

x = \frac{π}{3}

= \frac{cos ( \frac{π}{3} )}{1}

Simplify

\frac{cos ( \frac{π}{3} )}{1} : \frac{1}{2}

= \frac{1}{2}

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