Pertanyaan

x → π lim x − π sin x − sin π = ...

$x \to π lim \frac{sin x - sin π}{x - π} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat kembali sifat-sifat dan aturan berikut. Dari aturan di atas, maka diperoleh Dengan demikian, . Jadi, jawaban yang benar adalah B.

Ingat kembali sifat-sifat dan aturan berikut.

$limit as x rightwards arrow c of fraction numerator sin space a left parenthesis x minus c right parenthesis over denominator b left parenthesis x minus c right parenthesis end fraction equals limit as x rightwards arrow c of fraction numerator space a left parenthesis x minus c right parenthesis over denominator sin space b left parenthesis x minus c right parenthesis end fraction equals a over b$

Dari aturan di atas, maka diperoleh

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow pi of fraction numerator sin space x minus space sin space pi over denominator x minus pi end fraction end cell equals cell limit as x rightwards arrow pi of fraction numerator 2 space cos space begin display style 1 half end style left parenthesis x plus pi right parenthesis space sin space begin display style 1 half end style left parenthesis x minus pi right parenthesis over denominator x minus pi end fraction end cell row blank equals cell limit as x rightwards arrow pi of space 2 space cos space 1 half left parenthesis x plus pi right parenthesis times limit as x rightwards arrow pi of space fraction numerator sin space begin display style 1 half end style left parenthesis x minus pi right parenthesis over denominator x minus pi end fraction end cell row blank equals cell 2 space cos space 1 half left parenthesis pi plus pi right parenthesis times fraction numerator begin display style 1 half end style over denominator 1 end fraction end cell row blank equals cell 2 space cos space 1 half left parenthesis 2 pi right parenthesis times 1 half end cell row blank equals cell 2 times cos space pi times 1 half end cell row blank equals cell 2 times left parenthesis negative 1 right parenthesis times 1 half end cell row blank equals cell negative 1 end cell end table end style$

Dengan demikian, $limit as x rightwards arrow pi of fraction numerator sin space x minus sin space pi over denominator x minus pi end fraction equals negative 1$ .

Jadi, jawaban yang benar adalah B.