Nilai x→3πlimsin(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 ...

$-\frac12$
$\frac12$
$\frac12\sqrt2$
$\frac12\sqrt3$
$\frac32$

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.