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x→∞lim​2x2−x−2x2+2x−8​=...

Pertanyaan

begin mathsize 14px style 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 equals... end style

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: 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

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