Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize x\sin{\bigg(\dfrac{1}{x}\bigg)}}$

$=\,\,$ $\infty \times \sin{\bigg(\dfrac{1}{\infty}\bigg)}$

$=\,\,$ $\infty \times \sin{(0)}$

$=\,\,$ $\infty \times \sin{0}$

$=\,\,$ $\infty \times 0$

Methods

Change of variable

Learn how to evaluate the limit of the product of $x$ and sine of angle one divided by $x$ as $x$ tends to infinity by changing of the variable.

L’Hôpital’s Rule

Learn how to find the limit of $x$ times sine of multiplicative inverse of $x$ by the L’hospital’s rule as $x$ approaches infinity.

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