Pertanyaan

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

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

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Jadi, jawaban yang tepat adalah E.

$begin mathsize 14px style limit as straight x rightwards arrow 0 of fraction numerator sin left parenthesis 4 straight x right parenthesis plus sin left parenthesis 2 straight x right parenthesis over denominator 3 straight x squared cos left parenthesis straight x right parenthesis end fraction equals limit as straight x rightwards arrow 0 of fraction numerator 2 sin left parenthesis begin display style fraction numerator 4 straight x plus 2 straight x over denominator 2 end fraction end style right parenthesis space sin left parenthesis begin display style fraction numerator 4 straight x minus 2 straight x over denominator 2 end fraction end style right parenthesis over denominator 3 straight x squared cos left parenthesis straight x right parenthesis end fraction equals limit as straight x rightwards arrow 0 of fraction numerator 2 sin left parenthesis 3 straight x right parenthesis space sin left parenthesis straight x right parenthesis over denominator 3 straight x squared cos left parenthesis straight x right parenthesis end fraction equals 2 over 3 space. space limit as straight x rightwards arrow 0 of fraction numerator sin begin display style left parenthesis end style begin display style 3 end style begin display style straight x end style begin display style right parenthesis end style over denominator straight x end fraction space. space limit as straight x rightwards arrow 0 of fraction numerator tan begin display style left parenthesis end style begin display style straight x end style begin display style right parenthesis end style over denominator straight x end fraction equals 2 over 3. space 3 space. space 1 equals 2 end style$

Jadi, jawaban yang tepat adalah E.