Pertanyaan

Nilai dari: x → ∞ lim x 3 − 5 x 2 + 10 2 x 3 − 5

Nilai dari: $x \to \infty lim \frac{2 x ^{3} - 5}{x ^{3} - 5 x ^{2} + 10}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

Nilai dari

Nilai dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 straight x cubed minus 5 over denominator straight x cubed minus 5 straight x squared plus 10 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style$

Pembahasan

Ingat: . Jadi, Nilai dari

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 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow infinity of fraction numerator 2 straight x cubed minus 5 over denominator straight x cubed minus 5 straight x squared plus 10 end fraction end cell equals cell limit as straight x rightwards arrow infinity of fraction numerator 2 straight x cubed minus 5 over denominator straight x cubed minus 5 straight x squared plus 10 end fraction cross times fraction numerator begin display style 1 over x cubed end style over denominator 1 over x cubed end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 straight x cubed over denominator straight x cubed end fraction end style minus begin display style 5 over straight x cubed end style over denominator begin display style straight x cubed over straight x cubed end style minus begin display style fraction numerator 5 straight x squared over denominator straight x cubed end fraction end style plus begin display style 10 over straight x cubed end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 2 minus 5 over straight x cubed end style over denominator begin display style 1 minus 5 over straight x plus 10 over straight x cubed end style end fraction end cell row blank equals cell fraction numerator begin display style 2 minus 5 over infinity cubed end style over denominator begin display style 1 minus 5 over infinity plus 10 over infinity cubed end style end fraction end cell row blank equals cell fraction numerator 2 minus 0 over denominator 1 minus 0 plus 0 end fraction end cell row blank equals 2 end table$

Jadi, Nilai dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 straight x cubed minus 5 over denominator straight x cubed minus 5 straight x squared plus 10 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style$