Pertanyaan

Tentukan nilai limit fungsi berikut. F. x → 0 lim x 5 − x 3 − 4 x 2 x 4 + x 3 + 12 x 2

Tentukan nilai limit fungsi berikut.

F. $x \to 0 lim \frac{x ^{4} + x ^{3} + 12 x ^{2}}{x ^{5} - x ^{3} - 4 x ^{2}}$

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F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai .

nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 4 plus x cubed plus 12 x squared over denominator x to the power of 5 minus x cubed minus 4 x squared end fraction equals negative 3 end style$ .

Pembahasan

Dengan menggunakan metode pemfaktoran. Jadi, nilai .

Dengan menggunakan metode pemfaktoran.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator x to the power of 4 plus x cubed plus 12 x squared over denominator x to the power of 5 minus x cubed minus 4 x squared end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x squared end strike open parentheses x squared plus x plus 12 close parentheses over denominator up diagonal strike x squared end strike open parentheses x cubed minus x minus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x squared plus x plus 12 over denominator x cubed minus x minus 4 end fraction end cell row blank equals cell fraction numerator 0 squared plus 0 plus 12 over denominator 0 cubed minus 0 minus 4 end fraction end cell row blank equals cell fraction numerator 12 over denominator negative 4 end fraction end cell row blank equals cell negative 3 end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 4 plus x cubed plus 12 x squared over denominator x to the power of 5 minus x cubed minus 4 x squared end fraction equals negative 3 end style$ .