Hasil dari x→0lim​tan6xcos3xsin4x​ adalah ....

Pertanyaan

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 ....

  1. begin mathsize 14px style 0 end style

  2. 1 half

  3. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px 2 over size 14px 3 end cell end table

  4. undefined

  5. begin mathsize 14px style infinity end style

D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

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 begin mathsize 14px style 2 over 3 end style.

Jadi, jawaban yang tepat adalah C.

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