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

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

Learn how to solve limiti all'infinito problems step by step online. (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.