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

Jika ,  adalah bilangan real dan ,  maka tentukan !

  1. undefined 

  2. undefined 

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F. Ayudhita

Master Teacher

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Jawaban

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 size 14px lim with size 14px x size 14px rightwards arrow size 14px c below begin mathsize 14px style left parenthesis fraction numerator f open parentheses x close parentheses minus g left parenthesis x right parenthesis over denominator f open parentheses x close parentheses plus g left parenthesis x right parenthesis end fraction right parenthesis end style to the power of size 14px 2 size 14px equals fraction numerator begin mathsize 14px style left parenthesis L minus K right parenthesis squared end style over denominator begin mathsize 14px style left parenthesis L plus K right parenthesis squared end style end fraction.

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Pembahasan

Pembahasan
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Sifat yang digunakan: 1. ; 2. ; dan 3. . Dapat diperoleh, Jadi, .

Sifat yang digunakan:

1. begin mathsize 14px style limit as x rightwards arrow c of open parentheses f left parenthesis x right parenthesis close parentheses to the power of n equals open parentheses limit as x rightwards arrow c of f left parenthesis x right parenthesis close parentheses to the power of n end style;

2. undefined; dan

3. begin mathsize 14px style limit as x rightwards arrow c 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 c of f left parenthesis x right parenthesis end style.

 

Dapat diperoleh,

begin mathsize 14px style limit as x rightwards arrow c of open parentheses fraction numerator f open parentheses x close parentheses minus g left parenthesis x right parenthesis over denominator f open parentheses x close parentheses plus g left parenthesis x right parenthesis end fraction close parentheses squared equals open parentheses limit as x rightwards arrow c of fraction numerator f open parentheses x close parentheses minus g left parenthesis x right parenthesis over denominator f open parentheses x close parentheses plus g left parenthesis x right parenthesis end fraction close parentheses squared equals open parentheses fraction numerator limit as x rightwards arrow c of open parentheses f open parentheses x close parentheses minus g left parenthesis x right parenthesis close parentheses over denominator limit as x rightwards arrow c of open parentheses f open parentheses x close parentheses plus g left parenthesis x right parenthesis close parentheses end fraction close parentheses squared equals open parentheses fraction numerator limit as x rightwards arrow c of f left parenthesis x right parenthesis minus limit as x rightwards arrow c of g left parenthesis x right parenthesis over denominator limit as x rightwards arrow c of f left parenthesis x right parenthesis plus limit as x rightwards arrow c of g left parenthesis x right parenthesis end fraction close parentheses squared equals open parentheses fraction numerator L minus K over denominator L plus K end fraction close parentheses squared equals open parentheses L minus K close parentheses squared over open parentheses L plus K close parentheses squared end style  

Jadi, size 14px lim with size 14px x size 14px rightwards arrow size 14px c below begin mathsize 14px style left parenthesis fraction numerator f open parentheses x close parentheses minus g left parenthesis x right parenthesis over denominator f open parentheses x close parentheses plus g left parenthesis x right parenthesis end fraction right parenthesis end style to the power of size 14px 2 size 14px equals fraction numerator begin mathsize 14px style left parenthesis L minus K right parenthesis squared end style over denominator begin mathsize 14px style left parenthesis L plus K right parenthesis squared end style end fraction.

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Konsep Kilat

Konsep Limit

Sifat Limit

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