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

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

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

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

- \frac{2}{3}

Decimal

- 0.66666 \dots

Solution steps

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

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

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

x \to \frac{π}{2} + lim (\frac{tan ( x )}{\frac{3}{2 x - π}}) = - \frac{2}{3}

= - \frac{2}{3}

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