Pertanyaan

x → 4 π lim cos x − sin x 1 − 2 sin 2 x = ...

$x \to \frac{π}{4} lim \frac{1 - 2 sin ^{2} x}{cos x - sin x} = ...$

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Habis dalam

Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$limit as x rightwards arrow pi over 4 of fraction numerator 1 minus 2 space sin squared space x over denominator cos space x space minus space sin space x end fraction equals limit as x rightwards arrow 4 over pi of fraction numerator begin display style cos squared end style begin display style space end style begin display style minus end style begin display style space end style begin display style begin display style sin end style squared end style begin display style space end style begin display style x end style over denominator cos begin display style space end style begin display style x end style begin display style minus end style begin display style space end style begin display style sin end style begin display style space end style begin display style x end style end fraction equals limit as x rightwards arrow pi over 4 of fraction numerator open parentheses cos begin display style space end style begin display style x end style begin display style minus end style begin display style sin end style begin display style space end style begin display style x end style close parentheses begin display style open parentheses cos space x plus sin space x close parentheses end style over denominator cos begin display style space end style begin display style x end style begin display style minus end style begin display style sin end style begin display style space end style begin display style x end style end fraction equals limit as x rightwards arrow pi over 4 of open parentheses cos space x plus sin space x close parentheses$

$cos pi over 4 plus sin pi over 4 equals fraction numerator square root of 2 over denominator 2 end fraction plus fraction numerator square root of 2 over denominator 2 end fraction equals square root of 2$