Pertanyaan

x → 3 π lim sin ( 3 x − π ) tan ( 3 x − π ) cos ( 2 x ) = ....

$x \to \frac{π}{3} lim \frac{tan ( 3 x - π ) cos ( 2 x )}{sin ( 3 x - π )} = ....$

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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 :

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

Jadi, jawaban yang tepat adalah A.