Pertanyaan

Nilai x → 0 lim 1 − cos 4 x 1 − cos 2 x = ...

Nilai $x \to 0 lim \frac{1 - cos 2 x}{1 - cos 4 x}$ = ...

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Klaim

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

= ... Ingat!

$begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator 1 minus cos space 2 x over denominator 1 minus cos space 4 x end fraction end style$ = ...

Ingat!

$begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator 1 minus cos space 2 x over denominator 1 minus cos space 4 x end fraction equals limit as x rightwards arrow 0 of fraction numerator 1 minus cos space 2 x over denominator 1 minus open parentheses 2 space cos squared space 2 x minus 1 close parentheses end fraction equals limit as x rightwards arrow 0 of fraction numerator 1 minus cos space 2 x over denominator 2 minus 2 space cos squared space 2 x end fraction equals limit as x rightwards arrow 0 of fraction numerator 1 minus cos space 2 x over denominator 2 left parenthesis 1 minus 2 space cos squared space 2 x right parenthesis end fraction equals limit as x rightwards arrow 0 of fraction numerator open parentheses 1 minus cos space 2 x close parentheses over denominator 2 left parenthesis 1 minus 2 space cos squared space 2 x right parenthesis left parenthesis 1 plus 2 space cos squared space 2 x right parenthesis end fraction equals limit as x rightwards arrow 0 of fraction numerator open parentheses 1 minus cos space 2 x close parentheses over denominator 2 left parenthesis 1 minus 2 space cos squared space 2 x right parenthesis left parenthesis 1 plus 2 space cos squared space 2 x right parenthesis end fraction equals limit as x rightwards arrow 0 of fraction numerator 1 over denominator 2 left parenthesis 1 plus 2 space cos squared space 2 x right parenthesis end fraction equals fraction numerator 1 over denominator 2 open parentheses 1 plus 1 close parentheses end fraction equals 1 fourth end style$