Pertanyaan

x → 0 lim 3 x − x 2 6 x + x 2 − 3 x 3 = ....

$x \to 0 lim \frac{6 x + x ^{2} - 3 x ^{3}}{3 x - x ^{2}} = ....$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Pembahasan

Substitusi Karena didapat bentuk yang merupakan bentuk tak tentu, maka difaktorkan dahulu. Jadi, .

Substitusi

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 6 x plus x squared minus 3 x cubed over denominator 3 x minus x squared end fraction end cell equals cell fraction numerator 6 times 0 plus 0 squared minus 3 times 0 cubed over denominator 3 times 0 minus 0 squared end fraction end cell row blank equals cell 0 over 0 end cell end table$

Karena didapat bentuk yang merupakan bentuk tak tentu, maka difaktorkan dahulu.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 6 x plus x squared minus 3 x cubed over denominator 3 x minus x squared end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator x left parenthesis 6 plus x minus 3 x squared right parenthesis over denominator x left parenthesis 3 minus x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator left parenthesis 6 plus x minus 3 x squared right parenthesis over denominator left parenthesis 3 minus x right parenthesis end fraction end cell row blank equals cell fraction numerator 6 plus 0 minus 3 times 0 squared over denominator 3 minus 0 end fraction end cell row blank equals cell 6 over 3 end cell row blank equals 2 end table$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x plus x squared minus 3 x cubed over denominator 3 x minus x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank end table end style$ .