(i) Show that for every real number , the product satisfies . (ii) Hence determine…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

(i) Show that for every real number xx, the product sin⁡x cos⁡x\sin x\,\cos x satisfies −12≤sin⁡x cos⁡x≤12-\dfrac{1}{2}\le \sin x\,\cos x \le \dfrac{1}{2}. (ii) Hence determine lim⁡x→∞sin⁡x cos⁡xx\displaystyle \lim_{x \to \infty} \dfrac{\sin x\,\cos x}{x}.

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