Jika L, K adalah bilangan real dan x→climf(x)=L, ...

Pertanyaan

Jika $\style{font-size:14px}L$ , $\style{font-size:14px}K$ adalah bilangan real dan $\style{font-size:14px}{\lim_{x\rightarrow c}f\left(x\right)=L}$ , $\style{font-size:14px}{\lim_{x\rightarrow c}g\left(x\right)=K}$ maka tentukan $begin mathsize 14px style limit as x rightwards arrow c of open parentheses fraction numerator f open parentheses x close parentheses minus g open parentheses x close parentheses over denominator f open parentheses x close parentheses plus g open parentheses x close parentheses end fraction close parentheses squared end style$ !

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

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