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

The limit as x approaches pi/2 of (ln(sin(x)))/((pi-2x)^2) is -1/8

Popular >

limit as x approaches pi/2 of (ln(sin(x)))/((pi-2x)^2)

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

- \frac{1}{8}

Decimal Notation

- 0.125

Solution steps

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

Apply L'Hopital's Rule

: x \to \frac{π}{2} lim (\frac{cot ( x )}{- 4 ( π - 2 x )})

= x \to \frac{π}{2} lim (\frac{cot ( x )}{- 4 ( π - 2 x )})

Apply L'Hopital's Rule

: x \to \frac{π}{2} lim (\frac{- csc ^{2} ( x )}{8})

= x \to \frac{π}{2} lim (\frac{- csc ^{2} ( x )}{8})

Plug in the value

x = \frac{π}{2}

= \frac{- csc ^{2} ( \frac{π}{2} )}{8}

Simplify

\frac{- csc ^{2} ( \frac{π}{2} )}{8} : - \frac{1}{8}

= - \frac{1}{8}

x \to 3 lim ((2 x - 4)^{4} (x - 2))

x \to 4 lim (\frac{x ^{2} + 4}{5})

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

x \to \frac{π}{3} lim (\frac{1 - 2 cos ( x )}{π - 3 x})

x \to - 2 lim (3 x - 2)

What is the limit as x approaches pi/2 of (ln(sin(x)))/((pi-2x)^2) ?
The limit as x approaches pi/2 of (ln(sin(x)))/((pi-2x)^2) is -1/8