Question

Вычислить предел:)
$\lim_{x \to }\frac{\pi}{4}+0 tg((\frac{\pi}{8}+x) )^{tg2x}$

Answer 1

$\lim\limits_{x \to \frac{\pi}{4}+} (tg(\frac{\pi}{8} + x))^{tg(2x)}\\t = x - \frac{\pi}{4}\\\lim\limits_{t \to 0+} (tg(\frac{3\pi}{8} + t))^{tg(2t + \frac{\pi}{2})} = \lim\limits_{t \to 0+} (tg(\frac{3\pi}{8} + t))^{-ctg(2t)} = \lim\limits_{t \to 0+} (tg(\frac{3\pi}{8}))^{-ctg(2t)}$

$\lim\limits_{t \to 0+} (tg(\frac{3\pi}{8}))^{-ctg(2t)} = (tg(\frac{3\pi}{8}))^{-\lim\limits_{t \to 0+} ctg(2t)} = (tg(\frac{3\pi}{8}))^{-\infty} = 0$

Answer 2

Фото внизу..........