Question-210674

Question Number 210674 by noraell last updated on 15/Aug/24

Answered by BHOOPENDRA last updated on 16/Aug/24

f (x) = \frac{x^{2}}{k^{2} {- 1 + \sqrt{- 4 x^{4} - 4 x^{2} + 1}}}

{l i m x \to 0 \frac{s i n x}{x} = 1, l i m x \to 0 \frac{t a n x}{x} = 1}

c o n j u g a t e m u l t i p l i c a t i o n

\Rightarrow f (x) = \frac{- 1 - \sqrt{(- 4 x^{4} - 4 x^{2} + 1)}}{4 k^{2} (x^{2} + 1)}

\Rightarrow - l i m x \to 0 \frac{- 1 - \sqrt{(- 4 x^{4} - 4 x^{3} + 1)}}{4 k^{2} (x^{2} + 1)}

= \frac{1}{2 k^{2}} w h e r e k \neq 0