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Nilai x→3π​lim​sin(3x−π)tan(3x−π) cos(2x)​ adalah ...

Pertanyaan

Nilai limit as x rightwards arrow straight pi over 3 of fraction numerator tan open parentheses 3 x minus straight pi close parentheses space cos open parentheses 2 x close parentheses over denominator sin open parentheses 3 x minus straight pi close parentheses end fraction adalah ... 

  1. negative 1 half

  2. 1 half

  3. 1 half square root of 2

  4. 1 half square root of 3

  5. 3 over 2

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Substitusi langsung:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 3 of fraction numerator tan open parentheses 3 x minus straight pi close parentheses space cos open parentheses 2 x close parentheses over denominator sin open parentheses 3 x minus straight pi close parentheses end fraction end cell equals cell fraction numerator tan open parentheses 3 open parentheses begin display style straight pi over 3 end style close parentheses minus straight pi close parentheses space cos open parentheses 2 open parentheses straight pi over 3 close parentheses close parentheses over denominator sin open parentheses 3 open parentheses straight pi over 3 close parentheses minus straight pi close parentheses end fraction end cell row blank equals cell 0 over 0 left parenthesis tak space tentu right parenthesis end cell end table

Menjabarkan limit fungsi trigonometri:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 3 of fraction numerator tan open parentheses 3 x minus straight pi close parentheses space cos open parentheses 2 x close parentheses over denominator sin open parentheses 3 x minus straight pi close parentheses end fraction end cell equals cell limit as x rightwards arrow straight pi over 3 of fraction numerator tan open parentheses 3 x minus straight pi close parentheses over denominator sin open parentheses 3 x minus straight pi close parentheses end fraction times limit as x rightwards arrow straight pi over 3 of cos open parentheses 2 x close parentheses end cell row blank equals cell cos open parentheses fraction numerator 2 straight pi over denominator 3 end fraction close parentheses end cell row blank equals cell negative 1 half end cell end table end style 

Oleh karena itu, jawaban yang benar adalah A.

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