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

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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.

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