Roboguru

Nilai

Pertanyaan

Nilai limit as x rightwards arrow 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction close parentheses equals space... 

  1. negative 6 

  2. negative 4 

  3. negative 1 

  4. 2 

  5. 5 

Pembahasan Soal:

Mencari hasil limit:

limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction cross times fraction numerator 2 plus square root of x plus 2 end root over denominator 2 plus square root of x plus 2 end root end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction cross times fraction numerator 2 plus square root of x plus 2 end root over denominator 2 plus square root of x plus 2 end root end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 open parentheses 2 plus square root of x plus 2 end root close parentheses over denominator 2 minus square root of x plus 2 end root open parentheses 2 plus square root of x plus 2 end root close parentheses end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 open parentheses 2 plus square root of x plus 2 end root close parentheses over denominator negative left parenthesis x minus 2 right parenthesis end fraction close parentheses equals limit as x rightwards arrow thin space 2 of open parentheses negative open parentheses 2 plus square root of x plus 2 end root close parentheses close parentheses equals negative open parentheses 2 plus square root of 2 plus 2 end root close parentheses equals negative open parentheses 2 plus square root of 4 close parentheses equals negative open parentheses 2 plus 2 close parentheses equals negative 4 

Jadi, limit as x rightwards arrow thin space 2 of open parentheses fraction numerator x minus 2 over denominator 2 minus square root of x plus 2 end root end fraction close parentheses equals negative 4.

Dengan demikian, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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