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Jika L, K adalah bilangan real dan x→2lim​f(x)= L, x→2lim​g(x)=K maka tentukan x→2lim​(f(x)+g(x)f(x)−g(x)​)2.

Pertanyaan

Jika L, K adalah bilangan real dan limit as x rightwards arrow 2 of f left parenthesis x right parenthesis equals space straight Llimit as x rightwards arrow 2 of g left parenthesis x right parenthesis equals straight K maka tentukan limit as x rightwards arrow 2 of open parentheses fraction numerator f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end fraction close parentheses squared.

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai limit as x rightwards arrow 2 of open parentheses fraction numerator f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end fraction close parentheses squared equals open parentheses straight L minus straight K close parentheses squared over open parentheses straight L plus straight K close parentheses squared.

Pembahasan

Ingat sifat limit:

  1. limit as x rightwards arrow a of open parentheses f left parenthesis x right parenthesis plus-or-minus g left parenthesis x right parenthesis close parentheses equals limit as x rightwards arrow a of f left parenthesis x right parenthesis plus-or-minus limit as x rightwards arrow a of g left parenthesis x right parenthesis
  2. limit as x rightwards arrow a of open parentheses fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction close parentheses equals fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis end fraction
  3. limit as x rightwards arrow a of open parentheses f left parenthesis x right parenthesis times g left parenthesis x right parenthesis close parentheses equals limit as x rightwards arrow a of f left parenthesis x right parenthesis times limit as x rightwards arrow a of g left parenthesis x right parenthesis
  4. limit as x rightwards arrow a of open parentheses f left parenthesis x right parenthesis close parentheses to the power of straight n equals open parentheses limit as x rightwards arrow a of f left parenthesis x right parenthesis close parentheses to the power of n

 

limit as x rightwards arrow 2 of open parentheses fraction numerator f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end fraction close parentheses squared equals limit as x rightwards arrow 2 of open parentheses fraction numerator f squared left parenthesis x right parenthesis minus 2 f left parenthesis x right parenthesis times g left parenthesis x right parenthesis plus g squared left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus 2 f left parenthesis x right parenthesis times g left parenthesis x right parenthesis plus g squared left parenthesis x right parenthesis end fraction close parentheses equals fraction numerator limit as x rightwards arrow 2 of f squared left parenthesis x right parenthesis minus 2 times limit as x rightwards arrow 2 of f left parenthesis x right parenthesis times limit as x rightwards arrow 2 of g left parenthesis x right parenthesis plus limit as x rightwards arrow 2 of g squared left parenthesis x right parenthesis over denominator limit as x rightwards arrow 2 of f squared left parenthesis x right parenthesis plus 2 times limit as x rightwards arrow 2 of f left parenthesis x right parenthesis times limit as x rightwards arrow 2 of g left parenthesis x right parenthesis plus limit as x rightwards arrow 2 of g squared left parenthesis x right parenthesis end fraction equals fraction numerator open parentheses limit as x rightwards arrow 2 of f left parenthesis x right parenthesis close parentheses squared minus 2 times limit as x rightwards arrow 2 of f left parenthesis x right parenthesis times limit as x rightwards arrow 2 of g left parenthesis x right parenthesis plus open parentheses limit as x rightwards arrow 2 of g left parenthesis x right parenthesis close parentheses squared over denominator open parentheses limit as x rightwards arrow 2 of f left parenthesis x right parenthesis close parentheses squared plus 2 times limit as x rightwards arrow 2 of f left parenthesis x right parenthesis times limit as x rightwards arrow 2 of g left parenthesis x right parenthesis plus open parentheses limit as x rightwards arrow 2 of g left parenthesis x right parenthesis close parentheses squared end fraction equals fraction numerator straight L squared minus 2 straight L times straight K plus straight K squared over denominator straight L squared plus 2 straight L times straight K plus straight K squared end fraction equals open parentheses straight L minus straight K close parentheses squared over open parentheses straight L plus straight K close parentheses squared


Jadi nilai limit as x rightwards arrow 2 of open parentheses fraction numerator f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end fraction close parentheses squared equals open parentheses straight L minus straight K close parentheses squared over open parentheses straight L plus straight K close parentheses squared.

95

5.0 (6 rating)

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