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Nilai x → 0 lim ​ sin x + sin 3 x 4 x cos x ​ = ...

Nilai  = ...

  1. 4

  2. 3

  3. begin mathsize 12px style 4 over 3 end style

  4. 1

  5. begin mathsize 12px style 3 over 4 end style

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Y. Laksmi

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Jawaban terverifikasi

Jawaban

 begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator 4 x cos x over denominator sin x space plus space sin 3 x end fraction equals 1 end style

Pembahasan

Ingat! Jadi,

Ingat!

  • begin mathsize 12px style sin alpha plus sin beta equals 2 sin begin inline style 1 half end style open parentheses alpha plus beta close parentheses cos begin inline style 1 half end style open parentheses alpha minus beta close parentheses end style
  • begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator sin a x over denominator b x end fraction equals limit as x rightwards arrow 0 of fraction numerator begin display style a x end style over denominator begin display style sin b x end style end fraction equals a over b end style

begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator 4 x cos x over denominator sin space x plus sin 3 x end fraction  equals limit as x rightwards arrow 0 of fraction numerator 4 x cos x over denominator sin 3 x plus sin x end fraction  equals limit as x rightwards arrow 0 of fraction numerator 4 x cos x over denominator 2 sin 2 x times cos x end fraction  equals limit as x rightwards arrow 0 of fraction numerator 2 x over denominator sin space 2 x end fraction  equals 2 over 2  equals 1 end style

Jadi, begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator 4 x cos x over denominator sin x space plus space sin 3 x end fraction equals 1 end style

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Nilai x → 0 lim ​ x cos x sin 4 x + sin 2 x ​ = …

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