calculate-lim-x-pi-4-tan-x-tan-2x-

Question Number 188449 by mnjuly1970 last updated on 01/Mar/23

calculate

\lim_{x \to \frac{π}{4}} {(\tan (x))}^{\tan (2 x)} = ?

Answered by cortano12 last updated on 01/Mar/23

L = \lim_{x \to \frac{π}{4}} {[\tan x]}^{\tan 2 x}

L = e^{\lim_{x \to \frac{π}{4}} (\frac{\tan x - 1}{\tan 2 x})}

L = e^{\lim_{x \to \frac{π}{4}} \frac{\sin x - \cos x}{\cos x} . \frac{\sin 2 x}{(\cos x - \sin x) (\cos x + \sin x)}}

L = e^{\lim_{x \to \frac{π}{4}} [\frac{- \sin 2 x}{\cos x (\cos x + \sin x)}]}

L = e^{- (\frac{1}{\frac{1}{\sqrt{2}} (\sqrt{2})})} = \frac{1}{e}

Commented by mnjuly1970 last updated on 03/Mar/23

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