Pertanyaan

x → 2 lim ( x − 2 ) tan ( 3 x − 6 ) 1 − cos 2 ( x − 2 ) = ....

$x \to 2 lim \frac{1 - cos ^{2} ( x - 2 )}{( x - 2 ) tan ( 3 x - 6 )} = ....$

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Misal sehingga jika maka . Diperoleh Jadi, jawaban yang tepat adalah B.

Misal sehingga jika maka . Diperoleh

$begin mathsize 14px style space limit as straight x rightwards arrow 2 of space fraction numerator 1 minus cos squared left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x minus 2 right parenthesis space tan left parenthesis 3 straight x minus 6 right parenthesis end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 1 minus cos squared open parentheses straight x minus 2 close parentheses over denominator left parenthesis straight x minus 2 right parenthesis space tan left parenthesis 3 left parenthesis straight x minus 2 right parenthesis right parenthesis end fraction equals limit as straight y rightwards arrow 0 of fraction numerator sin squared left parenthesis straight y right parenthesis over denominator straight y space tan space left parenthesis 3 straight y right parenthesis end fraction equals limit as straight y rightwards arrow 0 of fraction numerator sin left parenthesis straight y right parenthesis over denominator straight y end fraction space. space limit as straight y rightwards arrow 0 of fraction numerator sin space left parenthesis straight y right parenthesis over denominator sin space left parenthesis 3 straight y right parenthesis end fraction equals space 1 space. space 1 third space equals space 1 third end style$

Jadi, jawaban yang tepat adalah B.