x→4πlimtan xsin (−x)+cos x=....

Pertanyaan

$limit as x rightwards arrow straight pi over 4 of fraction numerator sin space open parentheses negative x close parentheses plus cos space x over denominator tan space x end fraction equals....$

$0$
$\frac12\sqrt2$
$1$
$\sqrt2$
$\infty$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar dari pertanyaan tersebut adalah A.

Perhatikan bahwa : $\sin\;(-x)=-\;\sin\;x$ , sehingga soal dapat dicari seperti berikut :

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi over 4 of fraction numerator sin space open parentheses negative x close parentheses plus cos space x over denominator tan space x end fraction end cell equals cell limit as x rightwards arrow straight pi over 4 of fraction numerator negative sin space x plus cos space x over denominator tan space x end fraction end cell end table$

substitusikan $\frac\pi4$ pada fungsi, diperoleh :

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

Oleh karena itu, jawaban yang benar adalah A.