Pertanyaan

x → ∞ lim 5 x 3 − 4 x + 2 2 x 2 + 9 = ....

$x \to \infty lim \frac{2 x ^{2} + 9}{5 x ^{3} - 4 x + 2} =$ ....

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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: . 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 .

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

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