Pertanyaan

Tentukan nilai dari x → 2 lim x 2 − x − 2 6 − x − 2 2

Tentukan nilai dari $x \to 2 lim \frac{6}{x ^{2} - x - 2} - \frac{2}{x - 2}$

F. Freelancer9

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh $begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction equals negative 2 over 3 end style$ .

Pembahasan

Perhatikan perhitunganberikut. Jadi, diperoleh .

Perhatikan perhitungan berikut.

$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 fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction minus fraction numerator 2 over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction minus fraction numerator 2 left parenthesis x plus 1 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 minus 2 open parentheses x plus 1 close parentheses over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 minus 2 x minus 2 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 x plus 4 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 over denominator left parenthesis x plus 1 right parenthesis end fraction times fraction numerator left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 over denominator left parenthesis x plus 1 right parenthesis end fraction times 1 end cell row blank equals cell fraction numerator negative 2 over denominator 2 plus 1 end fraction times 1 end cell row blank equals cell negative 2 over 3 end cell end table end style$

Jadi, diperoleh $begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction equals negative 2 over 3 end style$ .