Pertanyaan

Hasil dari x → 0 lim tan 6 x cos 3 x sin 4 x adalah ....

Hasil dari $x \to 0 lim \frac{cos 3 x sin 4 x}{tan 6 x}$ adalah ....

D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat bahwa dan . Kemudian, perhatikan perhitungan berikut! Dengan demikian, hasil dari adalah . Jadi, jawaban yang tepat adalah C.

Ingat bahwa $limit as x rightwards arrow 0 of fraction numerator sin x over denominator x end fraction equals 1$ dan $limit as x rightwards arrow 0 of fraction numerator x over denominator tan x end fraction equals 1$ .

Kemudian, perhatikan perhitungan berikut!

$limit as x rightwards arrow 0 of fraction numerator cos 3 x sin 4 x over denominator tan 6 x end fraction equals limit as x rightwards arrow 0 of cos 3 x times limit as x rightwards arrow 0 of fraction numerator sin 4 x over denominator tan 6 x end fraction equals cos open parentheses 3 times 0 close parentheses times limit as x rightwards arrow 0 of open parentheses fraction numerator sin 4 x over denominator tan 6 x end fraction times fraction numerator 4 x over denominator 4 x end fraction times fraction numerator 6 x over denominator 6 x end fraction close parentheses equals cos 0 times limit as x rightwards arrow 0 of open parentheses fraction numerator sin 4 x over denominator 4 x end fraction times fraction numerator 6 x over denominator tan 6 x end fraction times fraction numerator 4 x over denominator 6 x end fraction close parentheses equals 1 times limit as x rightwards arrow 0 of fraction numerator sin 4 x over denominator 4 x end fraction times limit as x rightwards arrow 0 of fraction numerator 6 x over denominator tan 6 x end fraction times limit as x rightwards arrow 0 of fraction numerator 4 x over denominator 6 x end fraction equals limit as x rightwards arrow 0 of fraction numerator sin 4 x over denominator 4 x end fraction times limit as x rightwards arrow 0 of fraction numerator 6 x over denominator tan 6 x end fraction times limit as x rightwards arrow 0 of 4 over 6 equals 1 times 1 times 4 over 6 equals 2 over 3$

Dengan demikian, hasil dari $limit as x rightwards arrow 0 of fraction numerator cos 3 x sin 4 x over denominator tan 6 x end fraction$ adalah .

Jadi, jawaban yang tepat adalah C.