Pertanyaan

Nilai dari x → ∞ lim ( 4 x 2 − 8 x + 6 − ( 2 x − 3 ) ) = …

Nilai dari $x \to \infty lim (4 x^{2} - 8 x + 6 - (2 x - 3)) = \dots$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari limit tersebut adalah .

nilai dari limit tersebut adalah

Pembahasan

Perhatikan perhitungan limit tak hingga berikut. Cara I Cara II Jadi, nilai dari limit tersebut adalah .

Perhatikan perhitungan limit tak hingga berikut.

Cara I

Cara II

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 6 end root minus open parentheses 2 x minus 3 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 6 end root minus square root of open parentheses 2 x minus 3 close parentheses squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared minus 8 x plus 6 end root minus square root of 4 x squared minus 12 x plus 9 end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x squared minus 8 x plus 6 end root minus square root of 4 x squared minus 12 x plus 9 end root end cell row blank blank cell cross times fraction numerator square root of 4 x squared minus 8 x plus 6 end root plus square root of 4 x squared minus 12 x plus 9 end root over denominator square root of 4 x squared minus 8 x plus 6 end root plus square root of 4 x squared minus 12 x plus 9 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x squared minus 8 x plus 6 close parentheses minus open parentheses 4 x squared minus 12 x plus 9 close parentheses over denominator square root of 4 x squared minus 8 x plus 6 end root plus square root of 4 x squared minus 12 x plus 9 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 4 x minus 3 over denominator square root of 4 x squared minus 8 x plus 6 end root plus square root of 4 x squared minus 12 x plus 9 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 4 x over denominator x end fraction end style minus begin display style 3 over x end style over denominator square root of begin display style fraction numerator 4 x squared over denominator x squared end fraction end style minus begin display style fraction numerator 8 x over denominator x squared end fraction end style plus begin display style 6 over x squared end style end root plus square root of begin display style fraction numerator 4 x squared over denominator x squared end fraction end style minus begin display style fraction numerator 12 x over denominator x squared end fraction end style plus begin display style 9 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 4 minus 3 over x end style over denominator square root of begin display style 4 minus 8 over x plus 6 over x squared end style end root plus square root of begin display style 4 minus 12 over x plus 9 over x squared end style end root end fraction end cell row blank equals cell fraction numerator begin display style 4 minus 0 end style over denominator square root of begin display style 4 minus 0 plus 0 end style end root plus square root of begin display style 4 minus 0 plus 0 end style end root end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 plus 2 end fraction end cell row blank equals 1 end table$

Jadi, nilai dari limit tersebut adalah .