$\lim_{x\to\infty }\left(x\sin\left(\frac{\pi }{x}\right)\right)$

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Apprenez en ligne à résoudre des problèmes les limites de l'infini étape par étape.

$\lim_{x\to\infty }\left(\frac{\sin\left(\frac{\pi }{x}\right)}{\frac{1}{x}}\right)$

Apprenez en ligne à résoudre des problèmes les limites de l'infini étape par étape. (x)->(infinity)lim(xsin(pi/x)). Rewrite the product inside the limit as a fraction. If we directly evaluate the limit \lim_{x\to\infty }\left(\frac{\sin\left(\frac{\pi }{x}\right)}{\frac{1}{x}}\right) as x tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, and simplifying, the limit results in.