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Nilai x→3π​lim​cos2x2x+sin21​x​=....

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 fractionequals....

  1. 2 plus fraction numerator 4 straight pi over denominator 3 end fraction

  2. 2 minus fraction numerator 4 straight pi over denominator 3 end fraction

  3. 1 minus fraction numerator 4 straight pi over denominator 3 end fraction

  4. negative 1 minus fraction numerator 4 straight pi over denominator 3 end fraction

  5. negative 2 minus fraction numerator 4 straight pi over denominator 3 end fraction

A. Acfreelance

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah D

Ingat bahwa nilai straight pi equals 180 degree space maka space straight pi over 3 equals 60 degree

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.

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