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x→4π​lim​ 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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