When x approaches infinity, does Lim sin (x ^ n) / x ^ n exist? When x approaches infinity, does Lim sin (x ^ n) / x ^ n exist?

∵0≤|sin（x^n)|≤1
∴0≤|sin（x^n）/ x^n |≤|1/x^n| --》0
∵ LIM (x →∞) 1 / x ^ n = 0 by the pinch theorem:
∴lim(x→∞) sin（x^n） / x^n =0

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