Question

ㅤㅤㅤㅤπ(π - 2x) tan (x - (π/2))
Lim. _______________________
x → π/2. 2(x - π) cos² x​

Answer 1

Verified answer

[tex]\begin{aligned} \sf \lim_{x \to \frac{\pi}{2} } \frac{\pi(\pi - 2x) \: tan \: (x - \frac{\pi}{2}) }{2(x - \pi) \: {cos}^{2} \: x} \end{aligned}[/tex]

[tex]\begin{aligned} \sf &= \sf \lim_{x \to \frac{\pi}{2} } \bigg( \frac{2\pi}{2(x - \pi)}\bigg)\bigg( \frac{( \frac{\pi}{2} - x) \: tan - ( \frac{\pi}{2} - x) }{ {sin}^{2}( \frac{\pi}{2} - x) } \bigg) \\ \sf &= \sf \bigg( \frac{2\pi}{2( - \frac{\pi}{2}) }\bigg)\bigg( \frac{(1)( - 1)}{ {1}^{2} } \bigg)\\ \sf &= \sf \bigg( \frac{2\pi}{ - \frac{ 2\pi}{2} } \bigg) \bigg( \frac{ - 1}{1} \bigg) \\ \sf &= \sf ( - 2)( - 1)\\ \sf &= \sf 2\end{aligned} [/tex]