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limx →π1-4tan...

Question

$lim x \to π (1 - 4 tan x)^{cot x} =$

A

e^{- 4}

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B

e^{4}

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C

e^{2}

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D

e^{- 2}

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Solution

The correct option is A $e^{- 4}$
This is $1^{\infty}$ form,
$lim x \to π (1 - 4 tan x)^{cot x} = e^{lim x \to π (1 - 4 tan x - 1) cot x}$
$= e^{cot x (- 4 tan x)}$
$= e^{- 4}$

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