Pertanyaan

x → ∞ lim ( 4 x 2 + 2 x + 1 − 4 x 2 − 4 x + 5 ) = …

$x \to \infty lim (4 x^{2} + 2 x + 1 - 4 x^{2} - 4 x + 5) = \dots$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

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$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 open parentheses square root of 4 x squared plus 2 x plus 1 end root minus square root of 4 x squared minus 4 x plus 5 end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of left parenthesis square root of 4 x squared plus 2 x plus 1 end root minus square root of 4 x squared minus 4 x plus 5 end root right parenthesis times fraction numerator left parenthesis square root of 4 x squared plus 2 x plus 1 end root plus square root of 4 x squared minus 4 x plus 5 end root right parenthesis over denominator left parenthesis square root of 4 x squared plus 2 x plus 1 end root plus square root of 4 x squared minus 4 x plus 5 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x squared plus 2 x plus 1 close parentheses minus open parentheses 4 x squared minus 4 x plus 5 close parentheses over denominator square root of 4 x squared plus 2 x plus 1 end root plus square root of 4 x squared minus 4 x plus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 6 x minus 4 over denominator square root of 4 x squared plus 2 x plus 1 end root plus square root of 4 x squared minus 4 x plus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x open parentheses 6 minus begin display style 4 over x end style close parentheses over denominator square root of x squared end root square root of 4 plus begin display style 2 over x end style plus begin display style 1 over x squared end style end root plus square root of x squared end root square root of 4 minus begin display style 4 over x end style plus begin display style 5 over x squared end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator horizontal strike x open parentheses 6 minus begin display style 4 over x end style close parentheses over denominator horizontal strike x open parentheses square root of 4 plus begin display style 2 over x end style plus begin display style 1 over x squared end style end root plus square root of 4 minus begin display style 4 over x end style plus begin display style 5 over x squared end style end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 6 minus begin display style 4 over x end style over denominator square root of 4 plus begin display style 2 over x end style plus begin display style 1 over x squared end style end root plus square root of 4 minus begin display style 4 over x end style plus begin display style 5 over x squared end style end root end fraction end cell row blank equals cell fraction numerator 6 minus 0 over denominator square root of 4 plus 0 plus 0 end root plus square root of 4 minus 0 plus 0 end root end fraction end cell row blank equals cell 6 over 4 end cell row blank equals cell 3 over 2 end cell end table end style$

Jadi, .