The limit $\lim_{x\to\infty }\left(x\sin\left(\frac{\pi }{x}\right)\right)$ is indeterminate, because the limit of trigonometric functions as $x$ approaches infinity is indeterminate
indeterminate
Final answer to the problem
indeterminate
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The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.