Pertanyaan

Dengan mengalikan dengan faktor sekawan terlebih dahulu, tentukan nilai limit dari: (a) x → ∞ lim x 2 + 6 x + 2 − x 2 − 4 x + 1

Dengan mengalikan dengan faktor sekawan terlebih dahulu, tentukan nilai limit dari:

(a) $x \to \infty lim x^{2} + 6 x + 2 - x^{2} - 4 x + 1$

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Klaim

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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nilai dari adalah ..

nilai dari limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root

limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root

adalah

Pembahasan

Diketahui . Nilai dari : Jadi, nilai dari adalah ..

Diketahui limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root .

Nilai dari limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root :

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root end cell row blank equals cell limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root times fraction numerator square root of x squared plus 6 x plus 2 end root plus square root of x squared minus 4 x plus 1 end root over denominator square root of x squared plus 6 x plus 2 end root plus square root of x squared minus 4 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator x squared plus 6 x plus 2 minus x squared plus 4 x minus 1 over denominator square root of x squared plus 6 x plus 2 end root plus square root of x squared minus 4 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator 10 x plus 1 over denominator square root of x squared plus 6 x plus 2 end root plus square root of x squared minus 4 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator x open parentheses 10 plus begin display style 1 over x end style close parentheses over denominator x open parentheses square root of 1 plus begin display style 6 over x end style plus begin display style 2 over x squared end style end root plus square root of 1 minus begin display style 4 over x end style plus begin display style 1 over x squared end style end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator 10 plus begin display style 1 over x end style over denominator square root of 1 plus begin display style 6 over x end style plus begin display style 2 over x squared end style end root plus square root of 1 minus begin display style 4 over x end style plus begin display style 1 over x squared end style end root end fraction end cell row blank equals cell fraction numerator 10 plus 0 over denominator square root of 1 plus 0 plus 0 end root plus square root of 1 minus 0 plus 0 end root end fraction end cell row blank equals cell fraction numerator 10 over denominator square root of 1 plus square root of 1 end fraction end cell row blank equals cell fraction numerator 10 over denominator 1 plus 1 end fraction end cell row blank equals cell 10 over 2 end cell row blank equals 5 end table end style$

Jadi, nilai dari limit as x rightwards arrow infinity of space square root of x squared plus 6 x plus 2 end root minus square root of x squared minus 4 x plus 1 end root adalah ..