Pertanyaan

x → 0 lim tan 9 x − tan 3 x − sin x sin 7 x + tan 3 x − sin 5 x = ....

$x \to 0 lim \frac{sin 7 x + tan 3 x - sin 5 x}{tan 9 x - tan 3 x - sin x} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat kembali aturan limit fungsi trigonometri berikut. Dengan demikian nilai limit fungsi trigonometri pada soal adalah Jadi, jawaban yang tepat adalah E.

Ingat kembali aturan limit fungsi trigonometri berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin a x over denominator b x end fraction end cell equals cell a over b end cell row cell limit as x rightwards arrow 0 of fraction numerator tan a x over denominator b x end fraction end cell equals cell a over b end cell end table end style$

Dengan demikian nilai limit fungsi trigonometri pada soal adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of space fraction numerator sin 7 x plus tan 3 x minus sin 5 x over denominator tan 9 x minus tan 3 x minus sin x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator open parentheses sin 7 x plus tan 3 x minus sin 5 x close parentheses over denominator open parentheses tan 9 x minus tan 3 x minus sin x close parentheses end fraction times fraction numerator begin display style 1 over x end style over denominator 1 over x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator begin display style fraction numerator sin 7 x over denominator x end fraction end style plus begin display style fraction numerator tan 3 x over denominator x end fraction end style minus begin display style fraction numerator sin 5 x over denominator x end fraction end style over denominator begin display style fraction numerator tan 9 x over denominator x end fraction end style minus begin display style fraction numerator tan 3 x over denominator x end fraction end style minus begin display style fraction numerator sin x over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator 7 plus 3 minus 5 over denominator 9 minus 3 minus 1 end fraction end cell row blank equals cell 5 over 5 end cell row blank equals 1 end table end style$

Jadi, jawaban yang tepat adalah E.