Given-lim-x-0-f-x-1-f-x-2-find-the-value-of-lim-x-0-f-x-

Question Number 110440 by bemath last updated on 29/Aug/20

Given \lim_{x \to 0} (f (x) + \frac{1}{f (x)}) = 2, find the

value of \lim_{x \to 0} f (x) .

Answered by john santu last updated on 29/Aug/20

l e t g (x) = f (x) + \frac{1}{f (x)} & \lim_{x \to 0} g (x) = 2

\Leftrightarrow {(f (x))}^{2} - f (x) . g (x) + 1 = 0

b y q u a d r a t i c f o r m u l a

f (x) = \frac{g (x) \pm \sqrt{(g {(x)}^{2} - 4}}{2}

t h e n \lim_{x \to 0} f (x) = \lim_{x \to 0} (\frac{g (x) \pm \sqrt{(g {(x)}^{2} - 4}}{2})

= \frac{g (0) \pm \sqrt{(g {(0)}^{2} - 4}}{2} = \frac{2 \pm \sqrt{4 - 4}}{2} = 1

Commented by bemath last updated on 29/Aug/20

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