Pertanyaan

x → c lim ( x − c ) sin ( 3 x − 3 c ) 1 − cos ( x − c ) = ....

$x \to c lim \frac{1 - cos ( x - c )}{( x - c ) sin ( 3 x - 3 c )} = ....$

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

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

Misal sehingga jika maka .
Diperoleh:

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

Jadi, jawaban yang tepat adalah A.