Pertanyaan

Tentukan nilai dari soal di bawah ini 1. x → 0 lim x 6 − 5 x 4 + 6 x 2 x 3 + 4 x 2 − 12 x

Tentukan nilai dari soal di bawah ini
1. $x \to 0 lim \frac{x ^{3} + 4 x ^{2} - 12 x}{x ^{6} - 5 x ^{4} + 6 x ^{2}}$

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Pembahasan

jika substitusi nilai akan menghasilkan , sehingga bentuk limit perlu diubah substitusikan kembali nilai maka diperoleh jadi nilai

$begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x cubed plus 4 x squared minus 12 x over denominator x to the power of 6 minus 5 x to the power of 4 plus 6 x squared end fraction end style$ jika substitusi nilai akan menghasilkan , sehingga bentuk limit perlu diubah
$begin mathsize 14px style table row blank cell limit as x rightwards arrow 0 of fraction numerator x cubed plus 4 x squared minus 12 x over denominator x to the power of 6 minus 5 x to the power of 4 plus 6 x squared end fraction end cell row equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x open parentheses x squared plus 4 x minus 12 close parentheses over denominator up diagonal strike x open parentheses x to the power of 5 minus 5 x cubed plus 6 x squared close parentheses end fraction end cell row equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses x squared plus 4 x minus 12 close parentheses over denominator open parentheses x to the power of 5 minus 5 x cubed plus 6 x squared close parentheses end fraction end cell end table end style$

substitusikan kembali nilai maka diperoleh

jadi nilai $size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x to the power of size 14px 3 size 14px plus size 14px 4 size 14px x to the power of size 14px 2 size 14px minus size 14px 12 size 14px x over denominator size 14px x to the power of size 14px 6 size 14px minus size 14px 5 size 14px x to the power of size 14px 4 size 14px plus size 14px 6 size 14px x to the power of size 14px 2 end fraction equals infinity$