Question

Let ( L=lim _{x rightarrow 0}left{tan left(frac{pi}{4}-xright)right}^{1 / 1} )
Taking log on both sides
Fogl ( =log lim _{x rightarrow 0}left{tan left(frac{pi}{4}-xright)right}^{1 / x} )
( log C=lim _{x rightarrow 0} log left{tan left(frac{pi}{4}-xright)right}^{1 / x} )
Fogl ( left.=lim _{x rightarrow 0} frac{log f(m)(pi / y-x)}{x}right} )
( left{0,0 text { fosm } Rightarrow text { Apply } L^{prime}+10 text { pital's rule }right} )
a) ( log L=frac{lim _{x rightarrow 0}left(frac{-sec ^{2}(x mid y-x)}{tan (x / 4-x)}right)}{1} )
( Rightarrow log L=-lim _{x rightarrow 0} cot (pi / 4-x) times sec ^{2}(x)(x-x) )
( Rightarrow log L=-cot pi / 4 sec ^{2} pi / 4 )
J ( log L=-1 times(sqrt{2})^{2} )
( Rightarrow quad log L=-2 )
&) ( left[L=e^{-2} mid Rightarrow ) option right.

# lim tan (*_*) is equal to lim x =0 is equal to (a) 1 (C) e (b) e (d) e-2

Solution