Roboguru

Nilai  adalah ...

Nilai limit as x rightwards arrow 1 of space 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 adalah ...

  1. negative 2 

  2. negative 1 

  3. 0 

  4. 1 

  5. 2 

Jawaban:

Untuk mencari nilai limit di atas, kalikan fungsi dalam limit dengan bilangan rasional akar sekawan dari penyebut sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of space 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 cross times fraction numerator square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root over denominator square root of 2 plus 2 x end root plus square root of 6 minus 2 x end root end fraction end cell equals cell limit as x rightwards arrow 1 of space 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 2 plus 2 x minus open parentheses 6 minus 2 x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space 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 end cell row blank equals cell limit as x rightwards arrow 1 of space 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 end cell row blank equals cell fraction numerator 1 squared 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 over denominator 4 end fraction end cell row blank equals cell fraction numerator square root of 4 plus square root of 4 over denominator 4 end fraction end cell row blank equals cell 1. end cell end table 

Dengan demikian, jawaban yang benar adalah D.

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