lim-x-1-pi-pi-1-x-1-xpi-2-pi-2-

Question Number 184880 by mathlove last updated on 13/Jan/23

\lim_{x \to \frac{1}{π}} \frac{π^{- 1} - x}{\frac{1 - {(x π)}^{2}}{π^{2}}} = ?

Answered by aba last updated on 13/Jan/23

\lim_{x \to \frac{1}{π}} \frac{π^{- 1} - x}{\frac{1 - {(π x)}^{2}}{π^{2}}} = \lim_{x \to \frac{1}{π}} \frac{π^{2} (π^{- 1} - x)}{1 - {(π x)}^{2}} = \lim_{x \to \frac{1}{π}} \frac{π (1 - π x)}{1 - {(π x)}^{2}} = \lim_{x \to \frac{1}{π}} \frac{π}{1 + π x} = \frac{π}{2}

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