Nilai dari adalah ....

Pertanyaan

Nilai dari $begin mathsize 14px style lim subscript straight x rightwards arrow 3 end subscript open parentheses fraction numerator 2 over denominator straight x minus 3 end fraction minus fraction numerator 12 over denominator straight x squared minus 9 end fraction close parentheses end style$ adalah ....

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x = 3, maka didapatkan hasil . Bentuk ini merupakan salah satu bentuk tak tentu yang tidak dapat dicari secara langsung penyelesaiannya. Sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 3 of open parentheses fraction numerator 2 over denominator straight x minus 3 end fraction minus fraction numerator 12 over denominator straight x squared minus 9 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 3 of open parentheses fraction numerator 2 over denominator straight x minus 3 end fraction times fraction numerator straight x plus 3 over denominator straight x plus 3 end fraction minus fraction numerator 12 over denominator straight x squared minus 9 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 3 of open parentheses fraction numerator 2 open parentheses straight x plus 3 close parentheses over denominator straight x squared minus 9 end fraction minus fraction numerator 12 over denominator straight x squared minus 9 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 3 of open parentheses fraction numerator 2 straight x plus 6 over denominator straight x squared minus 9 end fraction minus fraction numerator 12 over denominator straight x squared minus 9 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator 2 straight x plus 6 minus 12 over denominator straight x squared minus 9 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator 2 straight x minus 6 over denominator straight x squared minus 9 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator 2 open parentheses straight x minus 3 close parentheses over denominator open parentheses straight x plus 3 close parentheses open parentheses straight x minus 3 close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator 2 over denominator straight x plus 3 end fraction end cell row blank equals cell fraction numerator 2 over denominator 3 plus 3 end fraction end cell row blank equals cell 2 over 6 end cell row blank equals cell 1 third end cell end table end style$

Jadi, jawaban yang tepat adalah C.