The number of points of discontinuity of $$f(x)=Ltn$$→∞⁡$$x2n$$−$$1x2n+1$$ is

$$fx=1$$−$$1x2n1+1x2n=1$$ , x<−$$10$$, $$x=$$−$$1$$−$$1$$, −$$11$$ ∴$$f(x)$$ is discontinuous at $$X=$$±$$1$$

Continuity

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Question

$The number of points of discontinuity of f (x) = {Lt}_{n \to \infty} [\frac{x^{2 n} - 1}{x^{2 n} + 1}] is$

Moderate

Solution

$f (x) = \frac{1 - \frac{1}{x^{2 n}}}{1 + \frac{1}{x^{2 n}}} = \{\begin{cases} 1, x < - 1 \\ 0, x = - 1 \\ - 1, - 1 < x < 1 \\ 0, x = 1 \\ 1 , x > 1 \end{cases}$ $∴ f (x) is discontinuous at X=±1$

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