Pertanyaan

Nilai dari x → 2 lim x 2 + 2 x − 8 x 2 + x − 6 adalah ...

Nilai dari $x \to 2 lim \frac{x ^{2} + x - 6}{x ^{2} + 2 x - 8}$ adalah ...

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

$limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction equals 5 over 6$ .

Pembahasan

Substitusi , diperoleh Hasilnya bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan metode pemfaktoran seperti di bawah ini Jadi, .

Substitusi x equals 2 , diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction end cell equals cell fraction numerator open parentheses 2 close parentheses squared plus open parentheses 2 close parentheses minus 6 over denominator open parentheses 2 close parentheses squared plus 2 open parentheses 2 close parentheses minus 8 end fraction end cell row blank equals cell fraction numerator 4 plus 2 minus 6 over denominator 4 plus 4 minus 8 end fraction end cell row blank equals cell 0 over 0 end cell end table$

Hasilnya bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan metode pemfaktoran seperti di bawah ini

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 3 close parentheses open parentheses x minus 2 close parentheses over denominator open parentheses x plus 4 close parentheses open parentheses x minus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 3 close parentheses over denominator open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 2 close parentheses plus 3 over denominator open parentheses 2 close parentheses plus 4 end fraction end cell row blank equals cell 5 over 6 end cell end table$

Jadi, $limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction equals 5 over 6$ .