Pertanyaan

N i l ai d a r i x → 0 lim x . tan 2 1 x 1 − cos 2 x = ....

$N i l ai d a r i x \to 0 lim \frac{1 - cos 2 x}{x . tan \frac{1}{2} x} = ....$

-4
-2
1
2
4

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Jawaban terverifikasi

Pembahasan

Nilai limit berikut adalah:

$limit as x rightwards arrow 0 of fraction numerator 1 minus cos space 2 x over denominator x. tan begin display style 1 half end style x end fraction equals limit as x rightwards arrow 0 of fraction numerator 1 minus left parenthesis 1 minus 2 sin squared x right parenthesis over denominator x. tan begin display style 1 half end style x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of fraction numerator 2 sin squared x over denominator x. tan begin display style 1 half end style x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of fraction numerator 2 sin x. sin x over denominator x end fraction. x over x fraction numerator 1 over denominator tan begin display style 1 half end style x end fraction. fraction numerator begin display style 1 half end style x over denominator begin display style 1 half end style x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of space 2 x.1.1.1. fraction numerator 1 over denominator begin display style 1 half end style x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space equals 4$