JS-lim-x-0-x-tan-x-sin-2x-cos-2x-1-

Question Number 107871 by john santu last updated on 13/Aug/20

\frac{✓ JS ✓}{♡}

\lim_{x \to 0} \sqrt{\frac{x \tan x}{\sin 2 x - \cos 2 x + 1}} ?

Commented by bemath last updated on 13/Aug/20

Answered by hgrocks last updated on 13/Aug/20

L^{2} = \lim_{x \to 0} \frac{x tanx}{2 sinx . cosx + {2 \sin}^{2} x}

= (\lim_{x \to 0} \frac{xtanx}{2 sinx}) . (\lim_{x \to 0} \frac{1}{cosx + sinx})

= \lim_{x \to 0} \frac{x}{2} . \frac{tanx}{x} . \frac{x}{sinx}

(Note : The Function Is not defined as x \to 0^{-})

So Only R . H . L exists

L = \lim_{x \to 0^{+}} \sqrt{L^{2}} = 0

★ hg ★

Commented by bemath last updated on 13/Aug/20

l i m i t e x i s t s i r . t h e r e s u l t 0 . i t c o r r e c t

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