x→π /2limtan 2xx π /2 =x→π /2lim 2 tan 2(π /2 x)2(x π /2) =x→π /2lim2 tan 2(π /2 x)2(π /2 x) =2 [∵x→ 0limtan xx=1] ...

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Limit

limx→π/2tan 2...

Question

$lim x \to \frac{π}{2} \frac{tan 2 x}{x - \frac{π}{2}}$ .

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Solution

$lim x \to π / 2 \frac{tan 2 x}{x - π / 2}$
$= lim x \to π / 2 \frac{- 2 tan 2 (π / 2 - x)}{2 (x - π / 2)}$
$= lim x \to π / 2 \frac{2 tan 2 (π / 2 - x)}{2 (π / 2 - x)}$
$= 2 [∵ lim x \to 0 \frac{tan x}{x} = 1]$

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