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

	Answered by BHOOPENDRA last updated on 16/Aug/24
	$f(x)=(x^2 /(k^2 {−1+(√(−4x^4 −4x^2 +1})) )) {lim x→0 ((sinx)/x)=1,limx→0 ((tanx)/x)=1} conjugate multiplication ⇒ f(x)=((−1−(√((−4x^4 −4x^2 +1))))/(4k^2 (x^2 +1))) ⇒−limx→0 ((−1−(√((−4x^4 −4x^3 +1))))/(4k^2 (x^2 +1))) =(1/(2k^2 )) where k≠0$
	$f (x) = \frac{x^{2}}{k^{2} {- 1 + \sqrt{- 4 x^{4} - 4 x^{2} + 1}}}$ ${l i m x \to 0 \frac{s i n x}{x} = 1, l i m x \to 0 \frac{t a n x}{x} = 1}$ $c o n j u g a t e m u l t i p l i c a t i o n$ $\Rightarrow f (x) = \frac{- 1 - \sqrt{(- 4 x^{4} - 4 x^{2} + 1)}}{4 k^{2} (x^{2} + 1)}$ $\Rightarrow - l i m x \to 0 \frac{- 1 - \sqrt{(- 4 x^{4} - 4 x^{3} + 1)}}{4 k^{2} (x^{2} + 1)}$ $= \frac{1}{2 k^{2}} w h e r e k \neq 0$
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