Pertanyaan

Tentukan nilai limit fungsi berikut! x → 2 lim ( x 2 + 2 x − 8 6 − x − 2 x − 1 )

Tentukan nilai limit fungsi berikut!

$x \to 2 lim (\frac{6}{x ^{2} + 2 x - 8} - \frac{x - 1}{x - 2})$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow 2 of space open parentheses fraction numerator 6 over denominator x squared plus 2 x minus 8 end fraction minus fraction numerator x minus 1 over denominator x minus 2 end fraction close parentheses end style$ adalah

Pembahasan

Dengan menerapkan konsep penyelesaian limit fungsi dengan metode pemfaktoran, diperoleh perhitungan sebagai berikut. Jadi, nilai adalah .

Dengan menerapkan konsep penyelesaian limit fungsi dengan metode pemfaktoran, diperoleh perhitungan sebagai 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 space open parentheses fraction numerator 6 over denominator x squared plus 2 x minus 8 end fraction minus fraction numerator x minus 1 over denominator x minus 2 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of space open parentheses fraction numerator 6 over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction minus fraction numerator x minus 1 over denominator x minus 2 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of space open parentheses fraction numerator 6 over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction minus fraction numerator open parentheses x minus 1 close parentheses open parentheses x plus 4 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator 6 minus open parentheses x minus 1 close parentheses open parentheses x plus 4 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator 6 minus open parentheses x squared plus 3 x minus 4 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator negative x squared minus 3 x plus 10 over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator negative open parentheses x squared plus 3 x minus 10 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator negative up diagonal strike open parentheses x minus 2 close parentheses end strike open parentheses x plus 5 close parentheses over denominator up diagonal strike open parentheses x minus 2 close parentheses end strike open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator negative open parentheses x plus 5 close parentheses over denominator open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses 2 plus 5 close parentheses over denominator open parentheses 2 plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator negative 7 over denominator 6 end fraction end cell row blank equals cell negative 7 over 6 end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 2 of space open parentheses fraction numerator 6 over denominator x squared plus 2 x minus 8 end fraction minus fraction numerator x minus 1 over denominator x minus 2 end fraction close parentheses end style$ adalah .