displaystyle limx → (π/4) (tan x)tan 2x equals

Question

displaystyle limx → (π/4) (tan x)tan 2x equals (A) e1 (B) e2 (C) e-1 (D) e-2

Tardigrade Admin · Accepted Answer

displaystyle limx → (π/4) (tan x)tan 2x (1∞ form) =e displaystyle limx → π/4(tan x-1)tan 2x =e displaystyle limx → π/4(1-tan x) (-2 tan x/(1+tan x)(1-tan x)) =e displaystyle limx → π/4(-2 tan x/1+tan x)=e-1

Q. $x \to \frac{π}{4} lim$ $(t an x)^{t an 2 x}$ equals

$e^{1}$

$e^{2}$

$e^{- 1}$

$e^{- 2}$

$x \to \frac{π}{4} lim$ $(t an x)^{t an 2 x}$ ( $1^{\infty}$ form)
$= e^{x \to π /4 lim (t an x - 1) t an 2 x}$
$= e^{x \to π /4 lim (1 - t an x) \frac{- 2 t an x}{( 1 + t an x ) ( 1 - t an x )}}$
$= e^{x \to π /4 lim \frac{- 2 t an x}{1 + t an x}} = e^{- 1}$

Q. x→4π​lim​ (tanx)tan2x equals

e1

e2

e−1

e−2