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x→0lim​3x3tanxsin4x​=....

Pertanyaan

limit as x rightwards arrow 0 of fraction numerator sin to the power of 4 x over denominator 3 x cubed tan x end fraction equals....

  1. 3

  2. 4 over 3

  3. 1 third

  4. negative 1 third

  5. negative 4 over 3

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C

Ingat sifat  limit berikut limit as x rightwards arrow 0 of fraction numerator sin x over denominator x end fraction equals 1.

Dengan menggunakan metode substitusi,diperoleh perhitungan sebagai berikut.

                          table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin to the power of 4 x over denominator 3 x cubed tan x end fraction end cell equals cell fraction numerator left parenthesis sin left parenthesis 0 right parenthesis right parenthesis to the power of 4 over denominator 3 left parenthesis 0 right parenthesis cubed. tan open parentheses 0 close parentheses end fraction end cell row blank equals cell 0 over 0 text (bentuk tak tentu) end text end cell end table

Karena dengan metode substitusi diperoleh perhitungan dalam bentuk tak tentu (0 over 0), maka selanjutnya diselesaikan dengan cara lain yaitu dengan mengubah bentuk fungsi trigonometri sebagi berikut. 

                          table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin to the power of 4 x over denominator 3 x cubed tan x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator sin to the power of 4 x over denominator 3 x cubed. begin display style fraction numerator sin x over denominator cos x end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin to the power of 4 x over denominator begin display style fraction numerator 3 x cubed. sin x over denominator cos x end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow 0 of sin to the power of 4 x divided by fraction numerator 3 x cubed. sin x over denominator cos x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin to the power of 4 x. cos x over denominator 3 x cubed. sin x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin to the power of up diagonal strike 4 end exponent x. cos x over denominator 3 x cubed. up diagonal strike sin x end strike end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin cubed x. cos x over denominator 3 x cubed end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses 1 third. fraction numerator sin x over denominator x end fraction. fraction numerator sin x over denominator x end fraction. fraction numerator sin x over denominator x end fraction close parentheses. limit as x rightwards arrow 0 of cos x end cell row blank blank cell open parentheses 1 third.1.1.1 close parentheses. cos open parentheses limit as x rightwards arrow 0 of x close parentheses end cell row blank equals cell 1 third. cos open parentheses 0 close parentheses end cell row blank equals cell 1 third.1 end cell row blank equals cell 1 third end cell end table       

Oleh karena itu, jawaban yang benar adalah C.

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