Pertanyaan

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

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

.

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

Pembahasan

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

Sifat yang digunakan:

1. ;

2. undefined ; dan

3. .

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

Latihan Bab

Konsep Kilat

Konsep Limit

Sifat Limit

Limit Fungsi Aljabar

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