Pertanyaan

Hasil dari x → 0 lim 4 − 4 cos 2 x tan 4 x sin x adalah ....

Hasil dari $x \to 0 lim \frac{tan 4 x sin x}{4 - 4 cos 2 x}$ adalah ....

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R. Mahmudah

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jika disubstitusi , maka didapat Oleh karena itu, didapat Kemudian, didapat bahwa Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

Jika disubstitusi , maka didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 2 x end cell equals cell 1 minus 2 sin squared invisible function application open parentheses 1 half times 2 x close parentheses end cell row blank equals cell 1 minus 2 sin squared invisible function application x end cell end table end style

Oleh karena itu, didapat

Kemudian, didapat bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 x sin invisible function application x over denominator 4 minus 4 cos invisible function application 2 x end fraction end cell equals cell limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 x sin invisible function application x over denominator 8 sin squared invisible function application x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 x up diagonal strike s i n invisible function application x end strike over denominator 8 sin invisible function application x up diagonal strike s i n invisible function application x end strike end fraction end cell row blank equals cell limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application 4 x over denominator 8 sin invisible function application x end fraction times fraction numerator 4 x over denominator 4 x end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application 4 x over denominator 4 x end fraction times fraction numerator x over denominator sin invisible function application x end fraction times 4 over 8 close parentheses end cell row blank equals cell 1 times 1 times 4 over 8 end cell row blank equals cell 1 half end cell end table end style$

Jadi, jawaban yang tepat adalah D.

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