Pertanyaan

Nilai dari x → 4 π lim cos x − sin x cos 2 x adalah ...

Nilai dari $x \to \frac{π}{4} lim \frac{cos 2 x}{cos x - sin x}$ adalah ...

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Jika pada limit dilakukan substitusi langsung akan menghasilkan , sehingga ubah dalam sudut rangkap menjadi , sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow straight pi over 4 of space fraction numerator cos space 2 x over denominator cos space x space minus space sin space x end fraction space end cell row blank equals cell space limit as x rightwards arrow straight pi over 4 of space fraction numerator cos squared x space minus space sin squared x over denominator cos space x space minus space sin space x end fraction end cell row blank equals cell space limit as x rightwards arrow straight pi over 4 of space fraction numerator open parentheses cos space x space minus space sin space x close parentheses open parentheses cos space x space plus space sin space x close parentheses over denominator left parenthesis cos space x space minus space sin space x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow straight pi over 4 of space cos space x space plus space sin space x end cell row blank equals cell space fraction numerator square root of 2 over denominator 2 end fraction space plus space fraction numerator square root of 2 over denominator 2 end fraction end cell row blank equals cell space square root of 2 end cell end table$