Nilai limx→0​tan3 21​xsin3 2x​​=​...​

Pertanyaan

Nilai table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin cubed space 2 x over denominator tan cubed space begin display style 1 half end style x end fraction end cell equals cell... end cell end table 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat!

Dalam limit trigonometri, berlaku:

  • limit as x rightwards arrow 0 of fraction numerator sin space a x over denominator tan space b x end fraction equals a over b 

Melalui metode substitusi, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin cubed space 2 x over denominator tan cubed space begin display style 1 half end style x end fraction end cell equals cell fraction numerator sin cubed space 2 left parenthesis 0 right parenthesis over denominator tan cubed space begin display style 1 half end style left parenthesis 0 right parenthesis end fraction end cell row blank equals cell fraction numerator sin cubed space 0 over denominator tan cubed space 0 end fraction end cell row blank equals cell 0 cubed over 0 cubed end cell row blank equals cell 0 over 0 end cell end table 

Karena merupakan bentuk tak tentu, maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin cubed space 2 x over denominator tan cubed space begin display style 1 half end style x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator sin space 2 x times sin space 2 x times sin space 2 x over denominator tan space begin display style 1 half end style x times tan space begin display style 1 half end style x times tan space begin display style 1 half end style x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin space 2 x over denominator tan space begin display style 1 half end style x end fraction times limit as x rightwards arrow 0 of fraction numerator sin space 2 x over denominator tan space begin display style 1 half end style x end fraction times limit as x rightwards arrow 0 of fraction numerator sin space 2 x over denominator tan space begin display style 1 half end style x end fraction end cell row blank equals cell fraction numerator 2 over denominator begin display style bevelled 1 half end style end fraction times fraction numerator 2 over denominator begin display style bevelled 1 half end style end fraction times fraction numerator 2 over denominator begin display style bevelled 1 half end style end fraction end cell row blank equals cell 4 times 4 times 4 end cell row blank equals 64 row blank equals cell 2 to the power of 6 end cell end table end style  

Oleh karena itu, jawaban yang tepat adalah D.

348

4.7 (14 rating)

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