Pertanyaan

Tentukan nilai dari: x → 1 lim x 2 − x x 2 + x − 2

Tentukan nilai dari:

$x \to 1 lim \frac{x ^{2} + x - 2}{x ^{2} - x}$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

Nilai

Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x squared plus straight x minus 2 over denominator straight x squared minus straight x end fraction end cell end table equals 3. end style$

Pembahasan

Mensubstitusikan nilai maka diperoleh: Karena hasilnyabentuk tak tentu yaitu maka dilanjutkan dengan menerapkan metode pemfaktoran. Jadi, Nilai

Mensubstitusikan nilai begin mathsize 14px style x equals 1 end style maka diperoleh:

Karena hasilnya bentuk tak tentu yaitu begin mathsize 14px style 0 over 0 end style maka dilanjutkan dengan menerapkan metode pemfaktoran.

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

Jadi, Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x squared plus straight x minus 2 over denominator straight x squared minus straight x end fraction end cell end table equals 3. end style$