Nilai dari x→2limx2−4x2+x−6=...

Pertanyaan

Nilai dari $begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared minus 4 end fraction equals... end style$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

diperoleh $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus x minus 6 over denominator x squared minus 4 end fraction end cell end table equals 5 over 4 end style$ .

Pembahasan

Langkah awal menentukan nilai limit adalah dengan mensubstitusi nilai x, maka

$begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared minus 4 end fraction equals 0 over 0 end style$

Setelah disubstitusi ternyata diperoleh bentuk tak tentu, sehingga untuk menyelesaikannya digunakan metode pemfaktoran

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared minus 4 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x plus 3 right parenthesis left parenthesis x minus 2 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator x plus 3 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 2 plus 3 over denominator 2 plus 2 end fraction end cell row blank equals cell 5 over 4 end cell row blank blank blank end table end style$

Jadi, diperoleh $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus x minus 6 over denominator x squared minus 4 end fraction end cell end table equals 5 over 4 end style$ .

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