x→4πlim 1−tan xsin x cos x=...

Pertanyaan

$limit as x rightwards arrow pi over 4 of space fraction numerator sin space x space cos space x over denominator 1 minus tan space x end fraction equals...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai $limit as x rightwards arrow pi over 4 of space fraction numerator sin space x space cos space x over denominator 1 minus tan space x end fraction$ adalah infinity

Pembahasan

Dengan menerapkan penyelesaian limit dengan metode substitusi, diperoleh hasil perhitungan sebagai berikut.

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

Jadi, nilai $limit as x rightwards arrow pi over 4 of space fraction numerator sin space x space cos space x over denominator 1 minus tan space x end fraction$ adalah infinity .

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