Solve-the-following-trigonometric-limit-lim-x-pi-4-5tg-x-

Question Number 24864 by A1B1C1D1 last updated on 27/Nov/17

Solve the following trigonometric limit :

\lim_{x \to \frac{π}{4}} (5 tg (x)) =

Answered by jota+ last updated on 28/Nov/17

\lim_{x \to 0} s i n x = 0 \lim_{x \to 0} c o s x = 1

\Rightarrow \underset{x \to 0}{\lim t a n} x = 0

h = x - \frac{π}{4}

5 \tan x =

= 5 \tan (\frac{π}{4} + h) = 5 \frac{1 + \tan h}{1 - \tan h} .

\underset{x \to π / 4}{\lim 5 t a n} x = 5 \lim_{h \to 0} \frac{1 + \tan h}{1 - \tan h} = 5

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