x→1limx−1x2−1=...

Pertanyaan

$limit as x rightwards arrow 1 of fraction numerator x squared minus 1 over denominator x minus 1 end fraction equals...$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

$limit as x rightwards arrow 1 of fraction numerator x squared minus 1 over denominator x minus 1 end fraction equals 2$ .

Pembahasan

Substitusi nilai x equals 1 , diperoleh

Hasilnya tidak terdefenisi, maka digunakan metode pemfaktoran yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator x squared minus 1 over denominator x minus 1 end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of open parentheses x plus 1 close parentheses end cell row blank equals cell open parentheses 1 close parentheses plus 1 end cell row blank equals 2 end table$

Jadi, $limit as x rightwards arrow 1 of fraction numerator x squared minus 1 over denominator x minus 1 end fraction equals 2$ .