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

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N. Puspita

Master Teacher

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 begin mathsize 14px style 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 equals 3 over 2 end style.

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Ingatlah bahwa . Selanjutnya kita akan menyelesaikan permasalahan limit di atas dengan cara mengalikan akar sekawan. Perhatikan bahwa Jadi, .

Ingatlah bahwa

begin mathsize 14px style limit as x rightwards arrow infinity of c over x to the power of n equals 0 end style.

Selanjutnya kita akan menyelesaikan permasalahan limit di atas dengan cara mengalikan akar sekawan.

Perhatikan bahwa

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, begin mathsize 14px style 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 equals 3 over 2 end style.

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