Pertanyaan

Tentukan nilai dari soal di bawah ini 2. x → 0 lim x 8 + 7 x 4 − 2 x 2 x 5 + 6 x 4 − x 2

Tentukan nilai dari soal di bawah ini
2. $x \to 0 lim \frac{x ^{5} + 6 x ^{4} - x ^{2}}{x ^{8} + 7 x ^{4} - 2 x ^{2}}$

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Pembahasan

akan menghasilkan nilai ketika disubstitusi , sehingga perlu diubah bentuk limitnya dengan faktorisasi Jadi nilai

$begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 5 plus 6 x to the power of 4 minus x squared over denominator x to the power of 8 plus 7 x to the power of 4 minus 2 x squared end fraction end style$ akan menghasilkan nilai ketika disubstitusi , sehingga perlu diubah bentuk limitnya dengan faktorisasi

$begin mathsize 14px style table attributes columnalign center left columnspacing 2px end attributes row equals cell limit as x rightwards arrow 0 of fraction numerator x to the power of 5 plus 6 x to the power of 4 minus x squared over denominator x to the power of 8 plus 7 x to the power of 4 minus 2 x squared end fraction end cell row equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x squared end strike open parentheses x cubed plus 6 x squared minus 1 close parentheses over denominator up diagonal strike x squared end strike open parentheses x to the power of 6 plus 7 x squared minus 2 close parentheses end fraction end cell row equals cell fraction numerator negative 1 over denominator negative 2 end fraction end cell row equals cell 1 half end cell end table end style$

Jadi nilai $size 14px lim with size 14px x size 14px rightwards arrow size 14px 0 below fraction numerator size 14px x to the power of size 14px 5 size 14px plus size 14px 6 size 14px x to the power of size 14px 4 size 14px minus size 14px x to the power of size 14px 2 over denominator size 14px x to the power of size 14px 8 size 14px plus size 14px 7 size 14px x to the power of size 14px 4 size 14px minus size 14px 2 size 14px x to the power of size 14px 2 end fraction equals 1 half$