x→1lim​x−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 

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 fraction numerator open parentheses 1 close parentheses squared minus 1 over denominator open parentheses 1 close parentheses minus 1 end fraction end cell row blank equals cell 0 over 0 end cell end table 

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

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