Pertanyaan

Selesaikan soal-soal berikut! x → ∞ lim x 2 − 3 2 x 2 − 5

Selesaikan soal-soal berikut!

$x \to \infty lim \frac{2 x ^{2} - 5}{x ^{2} - 3}$

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Jawaban terverifikasi

Jawaban

nilai dari adalah 2.

nilai dari $limit as x rightwards arrow infinity of fraction numerator 2 x squared minus 5 over denominator x squared minus 3 end fraction$ adalah 2.

Pembahasan

Bagilah limit fungsi tersebut dengan variabel pangkat tertinggi dan ingat bahwa : Dengan demikian nilai dari adalah 2.

Bagilah limit fungsi tersebut dengan variabel pangkat tertinggi dan ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 :

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

Dengan demikian nilai dari $limit as x rightwards arrow infinity of fraction numerator 2 x squared minus 5 over denominator x squared minus 3 end fraction$ adalah 2.