x→2πlim sin xtan 21x=...

Pertanyaan

$limit as x rightwards arrow straight pi over 2 of space fraction numerator tan space begin display style 1 half end style x over denominator sin space x end fraction equals... space$

$2\sqrt2$
$2$
$\sqrt2$
$1$
$\frac12$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat $\mathrm\pi=180^\circ\;$ .

maka

$straight pi over 4 equals fraction numerator 180 degree over denominator 4 end fraction equals 45 degree straight pi over 2 equals fraction numerator 180 degree over denominator 2 end fraction equals 90 degree$

Untuk mengerjakan soal limit fungsi trigonometri, kita subtitusi terlebih dahulu menjadi :

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 2 of space fraction numerator tan space begin display style 1 half end style x over denominator sin space x end fraction end cell equals cell fraction numerator tan space begin display style 1 half end style left parenthesis begin display style straight pi over 2 end style right parenthesis over denominator sin space left parenthesis begin display style straight pi over 2 end style right parenthesis end fraction end cell row blank equals cell fraction numerator tan space begin display style straight pi over 4 end style over denominator sin space begin display style straight pi over 2 end style end fraction end cell row blank equals cell fraction numerator tan space 45 degree over denominator sin space 90 degree end fraction end cell row blank equals cell 1 over 1 end cell row blank equals 1 end table$

Oleh karena itu, jawaban yang benar adalah D.