Pertanyaan

x → 2 lim sin ( 2 x − 4 ) tan ( 3 x − 6 ) = ...

$x \to 2 lim \frac{tan ( 3 x - 6 )}{sin ( 2 x - 4 )} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat kembali pemfaktoran,sifat limit dan limit fungsi trigonometri berikut. Dari aturan di atas, maka diperoleh Dengan demikian, . Jadi, jawaban yang benar adalah D.

Ingat kembali pemfaktoran, sifat limit dan limit fungsi trigonometri berikut.

$limit as x rightwards arrow c of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator limit as x rightwards arrow c of space f left parenthesis x right parenthesis over denominator limit as x rightwards arrow c of space g left parenthesis x right parenthesis end fraction$

$limit as x rightwards arrow c of fraction numerator sin space a left parenthesis x minus c right parenthesis over denominator b left parenthesis x minus c right parenthesis end fraction equals limit as x rightwards arrow c of fraction numerator space a left parenthesis x minus c right parenthesis over denominator sin space b left parenthesis x minus c right parenthesis end fraction equals a over b$

$limit as x rightwards arrow c of fraction numerator tan space a left parenthesis x minus c right parenthesis over denominator b left parenthesis x minus c right parenthesis end fraction equals limit as x rightwards arrow c of fraction numerator space a left parenthesis x minus c right parenthesis over denominator tan space b left parenthesis x minus c right parenthesis end fraction equals a over b$

Dari aturan di atas, maka diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator tan space left parenthesis 3 x minus 6 right parenthesis over denominator sin space left parenthesis 2 x minus 4 right parenthesis end fraction end cell equals cell limit as x rightwards arrow 2 of space fraction numerator tan space 3 left parenthesis x minus 2 right parenthesis over denominator sin space 2 left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator space begin display style fraction numerator tan space 3 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end style over denominator space begin display style fraction numerator sin space 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end style end fraction end cell row blank equals cell fraction numerator space limit as x rightwards arrow 2 of begin display style fraction numerator tan space 3 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end style over denominator limit as x rightwards arrow 2 of space begin display style fraction numerator sin space 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 3 over 1 end style over denominator begin display style 2 over 1 end style end fraction end cell row blank equals cell 3 over 1 times 1 half end cell row blank equals cell 3 over 2 end cell row blank equals cell 1 comma 5 end cell end table$

Dengan demikian, $limit as x rightwards arrow 2 of fraction numerator tan space left parenthesis 3 x minus 6 right parenthesis over denominator sin space left parenthesis 2 x minus 4 right parenthesis end fraction equals 1 comma 5$ .

Jadi, jawaban yang benar adalah D.