Pertanyaan

Tentukan nilaidari x → ∞ lim 2 x 2 + x + 2 x 2 − 5 x + 5 !

Tentukan nilai dari $x \to \infty lim \frac{x + 5}{2 x ^{2} + x + 2 x ^{2} - 5}$ !

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N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh $limit as x rightwards arrow infinity of space fraction numerator x plus 5 over denominator square root of 2 x squared plus x end root plus square root of 2 x squared minus 5 end root end fraction equals fraction numerator square root of 2 over denominator 4 end fraction$ .

Pembahasan

Gunakan konsep limit tak hingga. Perhatikan perhitungan berikut. Jadi, diperoleh .

Gunakan konsep limit tak hingga.

Perhatikan perhitungan berikut.

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

Jadi, diperoleh $limit as x rightwards arrow infinity of space fraction numerator x plus 5 over denominator square root of 2 x squared plus x end root plus square root of 2 x squared minus 5 end root end fraction equals fraction numerator square root of 2 over denominator 4 end fraction$ .