Pertanyaan

x → 0 lim cos 3 xtan 3 1 x cot 2 x − csc 2 x = ...

$x \to 0 lim \frac{cot 2 x - csc 2 x}{cos 3 xtan \frac{1}{3} x} = ...$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan hasil perhitungan sebagai berikut. Jadi, jawaban yang tepat adalah E.

Perhatikan hasil perhitungan sebagai berikut.

$begin mathsize 14px style limit as straight x rightwards arrow 0 of invisible function application fraction numerator cot invisible function application 2 straight x minus csc invisible function application 2 straight x over denominator cos invisible function application 3 xtan invisible function application 1 third straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application fraction numerator fraction numerator cos invisible function application 2 straight x over denominator sin invisible function application 2 straight x end fraction minus fraction numerator 1 over denominator sin invisible function application 2 straight x end fraction over denominator cos invisible function application 3 xtan invisible function application 1 third straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application fraction numerator cos invisible function application 2 straight x minus 1 over denominator sin invisible function application 2 xcos invisible function application 3 xtan invisible function application 1 third straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application fraction numerator negative 2 sin squared invisible function application straight x over denominator 2 sin invisible function application xcos invisible function application xcos invisible function application 3 xtan invisible function application 1 third straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application fraction numerator negative sin invisible function application straight x over denominator cos invisible function application xcos invisible function application 3 xtan invisible function application 1 third straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application fraction numerator negative 1 over denominator cos invisible function application xcos invisible function application 3 straight x end fraction cross times limit as straight x rightwards arrow 0 of invisible function application fraction numerator sin invisible function application straight x over denominator tan invisible function application 1 third straight x end fraction equals negative 1 cross times fraction numerator 1 over denominator 1 third end fraction equals negative 3 end style$

Jadi, jawaban yang tepat adalah E.