Nilai x→3πlimcos2x2x+sin21x=....

Pertanyaan

Nilai $limit as x rightwards arrow straight pi over 3 of fraction numerator 2 x plus sin begin display style 1 half end style x over denominator cos 2 x end fraction$ $=....$

$2 plus fraction numerator 4 straight pi over denominator 3 end fraction$
$2 minus fraction numerator 4 straight pi over denominator 3 end fraction$
$1 minus fraction numerator 4 straight pi over denominator 3 end fraction$
$negative 1 minus fraction numerator 4 straight pi over denominator 3 end fraction$
$negative 2 minus fraction numerator 4 straight pi over denominator 3 end fraction$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah D

Ingat bahwa nilai $\mathrm\pi=180^\circ\;\mathrm{maka}\;\frac{\mathrm\pi}3=60^\circ$

Dalam menentukan limit fungsi dengan metode subtitusi, maka diperoleh perhitungan sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 3 of fraction numerator 2 x plus sin begin display style 1 half end style x over denominator cos 2 x end fraction end cell equals cell fraction numerator 2 open parentheses straight pi over 3 close parentheses plus sin open parentheses begin display style 1 half end style cross times begin display style straight pi over 3 end style close parentheses over denominator cos open parentheses 2 cross times begin display style straight pi over 3 end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 straight pi over denominator 3 end fraction plus sin straight pi over 6 end style over denominator cos begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 straight pi over denominator 3 end fraction plus 1 half end style over denominator begin display style negative 1 half end style end fraction end cell row blank equals cell negative 2 open parentheses 2 straight pi over 3 plus 1 half close parentheses end cell row blank equals cell negative fraction numerator 4 straight pi over denominator 3 end fraction minus 1 end cell row blank equals cell negative 1 minus fraction numerator 4 straight pi over denominator 3 end fraction end cell end table$

Oleh karena itu, jawaban yang benar adalah D.