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Hitunglah nilai limit di bawah! x → ∞ lim 8 x 3 + x − 2 x 2 − 2 x − 5

Hitunglah nilai limit di bawah!

$x \to \infty lim \frac{x ^{2} - 2 x - 5}{8 x ^{3} + x - 2}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah 0.

nilai dari $begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator x squared minus 2 x minus 5 over denominator 8 x cubed plus x minus 2 end fraction end style$ adalah 0.

Pembahasan

Ingat: . Jadi, nilai dari adalah 0.

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator x squared minus 2 x minus 5 over denominator 8 x cubed plus x minus 2 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator x squared minus 2 x minus 5 over denominator 8 x cubed plus x minus 2 end fraction cross times fraction numerator begin display style 1 over x cubed end style over denominator x cubed end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style x squared over x cubed end style minus begin display style fraction numerator 2 x over denominator x cubed end fraction end style minus begin display style 5 over x cubed end style over denominator begin display style fraction numerator 8 x cubed over denominator x cubed end fraction end style plus begin display style x over x cubed end style minus begin display style 2 over x cubed end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style 1 over x minus 2 over x squared minus 5 over x cubed end style over denominator begin display style 8 plus 1 over x squared minus 2 over x cubed end style end fraction end cell row blank equals cell fraction numerator begin display style 1 over infinity minus 2 over infinity squared minus 5 over infinity cubed end style over denominator begin display style 8 plus 1 over infinity squared minus 2 over infinity cubed end style end fraction end cell row blank equals cell fraction numerator begin display style 0 minus 0 minus 0 end style over denominator begin display style 8 plus 0 minus 0 end style end fraction end cell row blank equals cell 0 over 8 end cell row blank equals 0 end table$

Jadi, nilai dari $begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator x squared minus 2 x minus 5 over denominator 8 x cubed plus x minus 2 end fraction end style$ adalah 0.