Pertanyaan

Hitunglah nilai limit di bawah ini. x → ∞ lim 2 x 2 − 5 − x + 3 .

Hitunglah nilai limit di bawah ini.

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

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nilai dari adalah .

nilai dari limit as x rightwards arrow infinity of square root of 2 x squared minus 5 end root minus square root of x plus 3 end root

adalah

Pembahasan

Untuk menyelesaiakan limit di atas, kalikan fungsi dengan akar sekawan fungsi. Setelah itu, bagi pembilang dan penyebut dengan pangkat tertinggi penyebut. Pangkat tertinggi penyebut soal limit di atas adalah sehingga: Dengan demikian, nilai dari adalah .

Untuk menyelesaiakan limit di atas, kalikan fungsi dengan akar sekawan fungsi.

$limit as x rightwards arrow infinity of square root of 2 x squared minus 5 end root minus square root of x plus 3 end root equals limit as x rightwards arrow infinity of square root of 2 x squared minus 5 end root minus square root of x plus 3 end root cross times open parentheses fraction numerator square root of 2 x squared minus 5 end root plus square root of x plus 3 end root over denominator square root of 2 x squared minus 5 end root plus square root of x plus 3 end root end fraction close parentheses equals limit as x rightwards arrow infinity of space fraction numerator open parentheses 2 x squared minus 5 close parentheses minus open parentheses x plus 3 close parentheses over denominator square root of 2 x squared minus 5 end root plus square root of x plus 3 end root end fraction equals limit as x rightwards arrow infinity of space fraction numerator 2 x squared minus x minus 8 over denominator square root of 2 x squared minus 5 end root plus square root of x plus 3 end root end fraction.$

Setelah itu, bagi pembilang dan penyebut dengan pangkat tertinggi penyebut. Pangkat tertinggi penyebut soal limit di atas adalah sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 2 x squared minus x minus 8 over denominator square root of 2 x squared minus 5 end root plus square root of x plus 3 end root end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 2 x squared over denominator x end fraction end style minus begin display style x over x end style minus begin display style 8 over x end style over denominator square root of begin display style fraction numerator 2 x squared over denominator x squared end fraction end style minus begin display style 5 over x squared end style end root plus square root of begin display style x over x squared end style plus begin display style 3 over x squared end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 x minus 1 minus 8 over x end style over denominator square root of begin display style 2 minus 5 over x squared end style end root plus square root of begin display style 1 over x plus 3 over x squared end style end root end fraction end cell row blank equals cell fraction numerator begin display style limit as x rightwards arrow infinity of space 2 x minus 1 minus 8 over x end style over denominator limit as x rightwards arrow infinity of square root of begin display style 2 minus 5 over x squared end style end root plus square root of begin display style 1 over x plus 3 over x squared end style end root end fraction end cell row blank equals cell fraction numerator infinity over denominator square root of 2 end fraction end cell row blank equals cell infinity. end cell end table$

Dengan demikian, nilai dari limit as x rightwards arrow infinity of square root of 2 x squared minus 5 end root minus square root of x plus 3 end root adalah .

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