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x→0lim​ x sin 2x1−cos2 3x​= ...

Pertanyaan

limit as x rightwards arrow 0 of space fraction numerator 1 minus cos squared space 3 x over denominator x space sin space 2 x end fraction equals space...                   

  1.  infinity   

  2. 9        

  3. 6 

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 comma 5 end cell end table            

  5. 2 comma 25 

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingatlah identitas Trigonometri

1 minus cos squared space x equals sin squared space x

mengakibatkan

1 minus cos squared space 3 x equals sin squared space 3 x number space number space horizontal ellipsis left parenthesis 1 right parenthesis.

Ingat juga sifat-sifat limit fungsi

  • limit as x rightwards arrow c of open square brackets f open parentheses x close parentheses times g open parentheses x close parentheses close square brackets equals limit as x rightwards arrow c of f open parentheses x close parentheses times limit as x rightwards arrow c of times g open parentheses x close parentheses
     
  • limit as x rightwards arrow c of fraction numerator sin space a x over denominator b x end fraction equals a over b
     
  • limit as x rightwards arrow c of fraction numerator sin space a x over denominator sin space b x end fraction equals a over b

Dengan menggunakan bentuk (1) dan sifat-sifat limit fungsi tersebut, didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of space fraction numerator 1 minus cos squared space 3 x over denominator x space sin space 2 x end fraction end cell equals cell limit as x rightwards arrow 0 of space fraction numerator sin squared space 3 x over denominator x space sin space 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses fraction numerator sin space 3 x over denominator x end fraction times fraction numerator sin space 3 x over denominator sin space 2 x end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin space 3 x over denominator x end fraction times limit as x rightwards arrow 0 of fraction numerator sin space 3 x over denominator sin space 2 x end fraction end cell row blank equals cell 3 over 1 times 3 over 2 end cell row blank equals cell 9 over 2 end cell row blank equals cell 4 comma 5 end cell end table             

Maka, limit as x rightwards arrow 0 of space fraction numerator 1 minus cos squared space 3 x over denominator x space sin space 2 x end fraction equals 4 comma 5

Oleh karena itu, jawaban yang benar adalah D.

99

4.5 (2 rating)

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