Pertanyaan

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

Jika L, K adalah bilangan real dan $x \to 2 lim f (x) = L$ , $x \to 2 lim g (x) = K$ maka tentukan $x \to 2 lim (\frac{f ( x ) - g ( x )}{f ( x ) + g ( x )})^{2}$ .

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai .

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: Jadi nilai .

Ingat sifat limit:

$limit as x rightwards arrow a of open parentheses fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction close parentheses equals fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis end fraction$

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

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