Pertanyaan

x → 0 lim sin x cos x 4 x + 3 x cos 2 x = ....

$x \to 0 lim \frac{4 x + 3 x cos 2 x}{sin x cos x} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Ingat bahwa . Kemudian, perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah B.

Ingat bahwa $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x over denominator sin x end fraction equals 1 end style$ .

Kemudian, perhatikan perhitungan berikut!

$begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator 4 x plus 3 x cos invisible function application 2 x over denominator sin invisible function application x cos invisible function application x end fraction equals limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator 4 x over denominator sin invisible function application x cos invisible function application x end fraction plus fraction numerator 3 x cos invisible function application 2 x over denominator sin invisible function application x cos invisible function application x end fraction close parentheses equals limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator x over denominator sin x end fraction times fraction numerator 4 over denominator cos invisible function application x end fraction plus fraction numerator x over denominator sin x end fraction times fraction numerator 3 cos invisible function application 2 x over denominator cos invisible function application x end fraction close parentheses equals limit as x rightwards arrow 0 of invisible function application fraction numerator x over denominator sin x end fraction times fraction numerator 4 over denominator cos invisible function application x end fraction plus limit as x rightwards arrow 0 of invisible function application fraction numerator x over denominator sin x end fraction times fraction numerator 3 cos invisible function application 2 x over denominator cos invisible function application x end fraction equals 1 times fraction numerator 4 over denominator cos invisible function application 0 end fraction plus 1 times fraction numerator 3 cos invisible function application 2 open parentheses 0 close parentheses over denominator cos invisible function application 0 end fraction equals 1 times 4 over 1 plus 1 times fraction numerator 3 times 1 over denominator 1 end fraction equals 4 plus 3 equals 7 end style$

Jadi, jawaban yang tepat adalah B.

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