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x→∞lim​5x3−4x+22x2+9​=....

Pertanyaan

limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 9 over denominator 5 x cubed minus 4 x plus 2 end fraction equals....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

 limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 9 over denominator 5 x cubed minus 4 x plus 2 end fraction equals 0.

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 2 x squared plus 9 over denominator 5 x cubed minus 4 x plus 2 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 9 over denominator 5 x cubed minus 4 x plus 2 end fraction cross times fraction numerator begin display style 1 over x cubed end style over denominator begin display style 1 over x cubed end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x squared over denominator x cubed end fraction end style plus begin display style 9 over x cubed end style over denominator begin display style fraction numerator 5 x cubed over denominator x cubed end fraction end style minus begin display style fraction numerator 4 x over denominator x cubed end fraction end style plus begin display style 2 over x cubed end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 over x plus 9 over x cubed end style over denominator begin display style 5 minus 4 over x squared plus 2 over x cubed end style end fraction end cell row blank equals cell fraction numerator begin display style 2 over infinity plus 9 over infinity cubed end style over denominator begin display style 5 minus 4 over infinity squared plus 2 over infinity cubed end style end fraction end cell row blank equals cell fraction numerator 0 plus 0 over denominator 5 minus 0 plus 0 end fraction end cell row blank equals cell 0 over 5 end cell row blank equals 0 end table

Jadi limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 9 over denominator 5 x cubed minus 4 x plus 2 end fraction equals 0.

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