Pertanyaan

Nilai x → 0 lim 2 x ( cos 12 x + cos 8 x ) sin 8 x + sin 4 x = ....

Nilai $x \to 0 lim \frac{sin 8 x + sin 4 x}{2 x ( cos 12 x + cos 8 x )} = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat: Jadi, jawaban yang tepat adalah E.

Ingat: $limit as x rightwards arrow 0 of equals fraction numerator sin space a x over denominator b x end fraction equals a over b$

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator sin space 8 x plus sin space 4 x over denominator 2 x open parentheses cos space 12 x plus cos space 8 x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator sin space 8 x plus sin space 4 x over denominator 2 x end fraction close parentheses open parentheses fraction numerator 1 over denominator cos space 12 x plus cos space 8 x end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator sin space 8 x over denominator 2 x end fraction plus fraction numerator sin space 4 x over denominator 2 x end fraction close parentheses open parentheses fraction numerator 1 over denominator cos space 12 x plus cos space 8 x end fraction close parentheses end cell row blank equals cell open parentheses 8 over 2 plus 4 over 2 close parentheses open parentheses fraction numerator 1 over denominator cos space 0 plus cos space 0 end fraction close parentheses end cell row blank equals cell 12 over 2 times fraction numerator 1 over denominator 1 plus 1 end fraction end cell row blank equals cell 6 times 1 half end cell row blank equals 3 end table end style$

Jadi, jawaban yang tepat adalah E.