2.4b.2-eg - x 2 sin 2 x = lim x → sin x 2 x 2 x 2 2 x ...

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Example Evaluate: lim x 0 sin 2 x sin x 2 . Solution: Note that as x 0, it follows that x 2 0 and 2 x 0, so that lim x 0 sin 2 x 2 x = 1 , and lim x 0 sin x 2 x 2 = 1 . Further, lim x 0 x 2 sin x 2 = lim x 0 1 (sin x 2 /x 2 ) = 1 1 = 1 . For the problem at hand, it follows that lim x 0 sin
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Unformatted text preview: x 2 sin 2 x = lim x → sin x 2 x 2 · x 2 2 x · 2 x sin 2 x ! = lim x → sin x 2 x 2 · lim x → x 2 · lim x → x 2 sin x 2 = 1 · · 1 = 0 ....
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