Pertanyaan

x → 0 lim tan ( 2 x ) − tan ( x ) sin ( 2 x ) − sin ( x ) = ....

$x \to 0 lim \frac{sin ( 2 x ) - sin ( x )}{tan ( 2 x ) - tan ( x )} = ....$

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Jadi, jawaban yang tepat adalah B.

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

Jadi, jawaban yang tepat adalah B.