Pertanyaan

x → 2 π lim 1 − sin x x cot 2 x = ....

$x \to \frac{π}{2} lim \frac{x cot ^{2} x}{1 - sin x} = ....$

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat kembali: Maka: Jadi, jawaban yang benar adalah E.

Ingat kembali:

$cot space straight x equals fraction numerator cos space straight x over denominator sin space straight x end fraction cos squared straight x equals 1 minus sin squared straight x$

Maka:

$limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x space cot squared straight x over denominator 1 minus sin space straight x end fraction equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x space. space begin display style fraction numerator cos squared straight x over denominator sin squared straight x end fraction end style space over denominator 1 minus sin space straight x end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator fraction numerator straight x times cos squared straight x over denominator sin squared straight x end fraction space over denominator 1 minus sin space straight x end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x times cos squared straight x over denominator sin squared straight x end fraction times fraction numerator 1 over denominator 1 minus sin space straight x end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x times cos squared straight x over denominator sin squared straight x times open parentheses 1 minus sin space straight x close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x times open parentheses 1 minus sin squared straight x close parentheses over denominator sin squared straight x times open parentheses 1 minus sin space straight x close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x times open parentheses 1 plus sin space straight x close parentheses times open parentheses 1 minus sin space straight x close parentheses over denominator sin squared straight x times open parentheses 1 minus sin space straight x close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow straight pi over 2 of space fraction numerator straight x times open parentheses 1 plus sin space straight x close parentheses over denominator sin squared straight x end fraction space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style straight pi over 2 end style times open parentheses 1 plus sin space begin display style straight pi over 2 end style close parentheses over denominator sin squared open parentheses begin display style straight pi over 2 end style close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style straight pi over 2 times open parentheses 1 plus 1 close parentheses end style over denominator 1 squared end fraction space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style straight pi over 2 times open parentheses 2 close parentheses end style over denominator 1 end fraction space space space space space space space space space space space space space space space space space space space space space equals straight pi$

Jadi, jawaban yang benar adalah E.