Roboguru

....

limit as x rightwards arrow 1 of fraction numerator x cubed minus x squared over denominator square root of 2 plus 2 x end root minus square root of 6 minus 2 x end root end fraction equals ....

  1. –2

  2. –1

  3. 0

  4. 1

  5. 2

Jawaban:

i)     Rasionalkan penyebut dari bentuk limit di atas

limit as x rightwards arrow 1 of fraction numerator x cubed minus x squared over denominator square root of 2 plus 2 x end root minus square root of 6 minus 2 x end root end fraction space equals space limit as x rightwards arrow 1 of fraction numerator x cubed minus x squared over denominator square root of 2 plus 2 x end root minus square root of 6 minus 2 x end root end fraction. fraction numerator square root of 2 plus 2 x end root begin display style plus end style square root of 6 minus 2 x end root over denominator square root of 2 plus 2 x end root begin display style plus end style square root of 6 minus 2 x end root end fraction  equals space limit as x rightwards arrow 1 of fraction numerator open parentheses x cubed minus x squared close parentheses begin display style open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses end style over denominator begin display style open parentheses square root of 2 plus 2 x end root close parentheses squared end style begin display style minus end style begin display style begin display style open parentheses square root of 6 minus 2 x end root close parentheses end style squared end style end fraction equals space limit as x rightwards arrow 1 of fraction numerator open parentheses x cubed minus x squared close parentheses begin display style open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses end style over denominator open parentheses 2 plus 2 x close parentheses begin display style minus end style begin display style open parentheses 6 minus 2 x close parentheses end style end fraction  equals space limit as x rightwards arrow 1 of fraction numerator open parentheses x cubed minus x squared close parentheses open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses over denominator 4 x minus 4 end fraction

ii)    Faktorkan bentuk-bentuk yang dapat difaktorkan

limit as x rightwards arrow 1 of fraction numerator open parentheses x cubed minus x squared close parentheses open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses over denominator 4 x minus 4 end fraction space equals space limit as x rightwards arrow 1 of fraction numerator x squared open parentheses x minus 1 close parentheses open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses over denominator 4 open parentheses x minus 1 close parentheses end fraction  equals space limit as x rightwards arrow 1 of fraction numerator begin display style x squared open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses end style over denominator begin display style 4 end style end fraction

iii)   Substitusikan x = 1 ke dalam bentuk limit

limit as x rightwards arrow 1 of fraction numerator x squared open parentheses square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root close parentheses over denominator 4 end fraction space equals space fraction numerator begin display style open parentheses 1 close parentheses squared end style begin display style open parentheses square root of 2 plus 2 open parentheses 1 close parentheses end root plus square root of 6 minus 2 open parentheses 1 close parentheses end root close parentheses end style over denominator 4 end fraction space equals space fraction numerator 1 open parentheses square root of 4 plus square root of 4 close parentheses over denominator 4 end fraction equals space 4 over 4 space equals space 1

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