Pertanyaan

Tentukan nilai limit fungsi berikut ini! x → ∞ lim x 2 + 5 ( 2 x − 5 ) 2

Tentukan nilai limit fungsi berikut ini!

$x \to \infty lim \frac{( 2 x - 5 ) ^{2}}{x ^{2} + 5}$

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

nilai adalah 4.

nilai $begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator open parentheses 2 x minus 5 close parentheses squared over denominator x squared plus 5 end fraction end style$ adalah 4.

Pembahasan

Dengan menerapkan konsep limit tak hingga, diperoleh hasil perhitungan sebagai berikut. Jadi, nilai adalah 4.

Dengan menerapkan konsep limit tak hingga, diperoleh hasil perhitungan sebagai berikut.

$begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator open parentheses 2 x minus 5 close parentheses squared over denominator x squared plus 5 end fraction equals limit as x rightwards arrow infinity of fraction numerator 4 x squared minus 20 x plus 25 over denominator x squared plus 5 end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 4 x squared over denominator x squared end fraction end style minus begin display style fraction numerator 20 x over denominator x squared end fraction end style plus begin display style 25 over x squared end style over denominator begin display style x squared over x squared end style plus begin display style 5 over x squared end style end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style 4 minus 20 over x plus 25 over x squared end style over denominator begin display style 1 plus 5 over x squared end style end fraction equals fraction numerator 4 minus 0 plus 0 over denominator 1 plus 0 end fraction equals 4 over 1 equals 4 end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator open parentheses 2 x minus 5 close parentheses squared over denominator x squared plus 5 end fraction end style$ adalah 4.