Pertanyaan

Diketahui , maka nilai dari 2 p − q = ....

Diketahui $begin mathsize 14px style lim subscript straight x rightwards arrow 2 end subscript fraction numerator square root of straight p open parentheses straight x minus 2 close parentheses plus straight q end root minus 5 over denominator straight x minus 2 end fraction equals negative 2 over 5 end style$ , maka nilai dari $2 p - q =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x = 2 , maka didapatkan hasil Didapat bentuk limit yang jika dilakukan substitusi x = 2 , maka penyebutnya bernilai 0. Tetapi, nilai limitnya ada. Maka haruslah pembilangnya juga bernilai 0 jika disubstitusi x = 2 . Sehingga Maka didapat bahwa Sehingga Jadi, jawaban yang tepat adalah E.

Perhatikan bahwa jika dilakukan substitusi x = 2, maka didapatkan hasil

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of straight p open parentheses straight x minus 2 close parentheses plus straight q end root minus 5 over denominator straight x minus 2 end fraction end cell equals cell fraction numerator square root of straight p open parentheses 2 minus 2 close parentheses plus straight q end root minus 5 over denominator 2 minus 2 end fraction end cell row blank equals cell fraction numerator square root of straight p open parentheses 0 close parentheses plus straight q end root minus 5 over denominator 0 end fraction end cell row blank equals cell fraction numerator square root of straight q minus 5 over denominator 0 end fraction end cell end table end style$

Didapat bentuk limit yang jika dilakukan substitusi x = 2, maka penyebutnya bernilai 0. Tetapi, nilai limitnya ada.
Maka haruslah pembilangnya juga bernilai 0 jika disubstitusi x = 2. Sehingga
begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of straight q minus 5 end cell equals 0 row cell square root of straight q end cell equals 5 row straight q equals 25 end table end style

Maka didapat bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 2 of fraction numerator square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root minus 5 over denominator straight x minus 2 end fraction end cell equals cell negative 2 over 5 end cell row cell limit as straight x rightwards arrow 2 of open parentheses fraction numerator square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root minus 5 over denominator straight x minus 2 end fraction times fraction numerator square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root plus 5 over denominator square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root plus 5 end fraction close parentheses end cell equals cell negative 2 over 5 end cell row cell limit as straight x rightwards arrow 2 of fraction numerator open parentheses straight p open parentheses straight x minus 2 close parentheses plus 25 close parentheses minus 25 over denominator open parentheses straight x minus 2 close parentheses open parentheses square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root plus 5 close parentheses end fraction end cell equals cell negative 2 over 5 end cell row cell limit as straight x rightwards arrow 2 of fraction numerator straight p open parentheses straight x minus 2 close parentheses over denominator open parentheses straight x minus 2 close parentheses open parentheses square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root plus 5 close parentheses end fraction end cell equals cell negative 2 over 5 end cell row cell limit as straight x rightwards arrow 2 of fraction numerator straight p over denominator square root of straight p open parentheses straight x minus 2 close parentheses plus 25 end root plus 5 end fraction end cell equals cell negative 2 over 5 end cell row cell fraction numerator straight p over denominator square root of straight p open parentheses 2 minus 2 close parentheses plus 25 end root plus 5 end fraction end cell equals cell negative 2 over 5 end cell row cell fraction numerator straight p over denominator square root of straight p open parentheses 0 close parentheses plus 25 end root plus 5 end fraction end cell equals cell negative 2 over 5 end cell row cell fraction numerator straight p over denominator square root of 25 plus 5 end fraction end cell equals cell negative 2 over 5 end cell row cell fraction numerator straight p over denominator 5 plus 5 end fraction end cell equals cell negative 2 over 5 end cell row cell straight p over 10 end cell equals cell negative 2 over 5 end cell row straight p equals cell negative 2 over 5 open parentheses 10 close parentheses end cell row straight p equals cell negative 4 end cell end table end style$

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight p minus straight q end cell equals cell 2 open parentheses negative 4 close parentheses minus 25 end cell row blank equals cell negative 8 minus 25 end cell row blank equals cell negative 33 end cell end table end style

Jadi, jawaban yang tepat adalah E.