Pertanyaan

Hitunglah! x → ∞ lim 2 x − 1 x 2 − 2 x + 1 x 2 = ...

Hitunglah!

$x \to \infty lim \frac{x ^{2}}{2 x - 1} - \frac{x ^{2}}{2 x + 1} = ...$

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Jawaban terverifikasi

Jawaban

hasil dari adalah

hasil dari $limit as x rightwards arrow infinity of fraction numerator x squared over denominator 2 x minus 1 end fraction minus fraction numerator x squared over denominator 2 x plus 1 end fraction$ adalah 1 half.

Pembahasan

Perhatikan penghitungan berikut! Jadi, hasil dari adalah

Perhatikan penghitungan berikut!

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

Jadi, hasil dari $limit as x rightwards arrow infinity of fraction numerator x squared over denominator 2 x minus 1 end fraction minus fraction numerator x squared over denominator 2 x plus 1 end fraction$ adalah 1 half.