Pertanyaan

Diketahui f ( x ) adalah sebuah fungsi dengan dengan L adalah suatu bilangan real. Jika , maka L = ....

Diketahui $f (x)$ adalah sebuah fungsi dengan dengan $L$ adalah suatu bilangan real. Jika $begin mathsize 14px style limit as x rightwards arrow 3 of invisible function application square root of fraction numerator open parentheses x minus 5 close parentheses squared over denominator f open parentheses x close parentheses open parentheses x minus 2 close parentheses end fraction end root equals 4 end style$ , maka $L =$ ....

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Jawaban terverifikasi

Jawaban

jawabannya adalah E.

Pembahasan

Perhatikan bahwa Jadi, jawabannya adalah E.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of invisible function application square root of fraction numerator open parentheses x minus 5 close parentheses squared over denominator f open parentheses x close parentheses open parentheses x minus 2 close parentheses end fraction end root end cell equals 4 row cell square root of limit as x rightwards arrow 3 of invisible function application open parentheses fraction numerator open parentheses x minus 5 close parentheses squared over denominator f open parentheses x close parentheses open parentheses x minus 2 close parentheses end fraction close parentheses end root end cell equals 4 row cell square root of fraction numerator limit as x rightwards arrow 3 of invisible function application open parentheses x minus 5 close parentheses squared over denominator limit as x rightwards arrow 3 of invisible function application open parentheses f open parentheses x close parentheses open parentheses x minus 2 close parentheses close parentheses end fraction end root end cell equals 4 row cell square root of fraction numerator open parentheses limit as x rightwards arrow 3 of invisible function application open parentheses x minus 5 close parentheses close parentheses squared over denominator limit as x rightwards arrow 3 of invisible function application f open parentheses x close parentheses times limit as x rightwards arrow 3 of invisible function application open parentheses x minus 2 close parentheses end fraction end root end cell equals 4 row cell square root of fraction numerator open parentheses 3 minus 5 close parentheses squared over denominator L times open parentheses 3 minus 2 close parentheses end fraction end root end cell equals 4 row cell square root of fraction numerator open parentheses negative 2 close parentheses squared over denominator L times 1 end fraction end root end cell equals 4 row cell square root of 4 over L end root end cell equals 4 row cell 4 over L end cell equals 16 row cell 4 over 16 end cell equals L row L equals cell 1 fourth end cell end table end style$

Jadi, jawabannya adalah E.