Pertanyaan

x → ∞ lim 2 x 2 − x − 2 x 2 + 2 x − 8 = ...

$x \to \infty lim \frac{x ^{2} + 2 x - 8}{2 x ^{2} - x - 2} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 2 x minus 8 over denominator 2 x squared minus x minus 2 end fraction end cell end table equals 1 half$

Pembahasan

Ingat: . Jadi

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 .

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

Jadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 2 x minus 8 over denominator 2 x squared minus x minus 2 end fraction end cell end table equals 1 half$