Pertanyaan

Nilai dari x → 0 lim sin 5 x − 2 x tan 4 x x + sin x tan 3 x adalah ....

Nilai dari $x \to 0 lim \frac{x + sin x tan 3 x}{sin 5 x - 2 x tan 4 x}$ adalah ....

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Klaim

D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah B.

Perhatikan perhitungan berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator x plus sin x tan 3 x over denominator sin 5 x minus 2 x tan 4 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x plus sin x tan 3 x over denominator sin 5 x minus 2 x tan 4 x end fraction times fraction numerator 1 over x over denominator 1 over x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 1 plus fraction numerator sin x over denominator x end fraction times tan 3 x over denominator fraction numerator sin 5 x over denominator x end fraction minus 2 tan 4 x end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow 0 of 1 plus limit as x rightwards arrow 0 of fraction numerator sin x over denominator x end fraction times limit as x rightwards arrow 0 of tan 3 x over denominator limit as x rightwards arrow 0 of fraction numerator sin 5 x over denominator x end fraction minus 2 limit as x rightwards arrow 0 of tan 4 x end fraction end cell row blank equals cell fraction numerator 1 plus 1 over 1 times 0 over denominator 5 over 1 minus 2 times 0 end fraction end cell row blank equals cell 1 fifth end cell end table end style$

Jadi, jawaban yang tepat adalah B.