What is the limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6) ?

The limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6) is (sqrt(3))/2

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limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6)

x \to \frac{π}{6} lim (\frac{sin ( x ) - sin ( \frac{π}{6} )}{x - \frac{π}{6}})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

x \to \frac{π}{6} lim (\frac{sin ( x ) - sin ( \frac{π}{6} )}{x - \frac{π}{6}})

Apply L'Hopital's Rule

: x \to \frac{π}{6} lim (\frac{cos ( x )}{1})

= x \to \frac{π}{6} lim (\frac{cos ( x )}{1})

Plug in the value

x = \frac{π}{6}

= \frac{cos ( \frac{π}{6} )}{1}

Simplify

\frac{cos ( \frac{π}{6} )}{1} : \frac{3}{2}

= \frac{3}{2}

\int 20 tan (2 x) sec^{2} (2 x) d x

\frac{d}{d x} (sin (ln (4 x)))

e^{- 4 x^{2}}

x \to - 1 lim (16 - 4 x)

\int ((y) ln (1 + y)) d y

What is the limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6) ?
The limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6) is (sqrt(3))/2