Tentukan nilai limit berikut: 1. x→1lim x−2x2+1

Pertanyaan

Tentukan nilai limit berikut:

1. $begin mathsize 14px style limit as x rightwards arrow 1 of space fraction numerator x squared plus 1 over denominator x minus 2 end fraction end style$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh $begin mathsize 14px style limit as x rightwards arrow 1 of space fraction numerator x squared plus 1 over denominator x minus 2 end fraction equals negative 2 end style$ .

Pembahasan

Gunakan konsep limit bentuk aljabar dan limit pada fungsi pecahan.

Perhatikan perhitungan berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 1 of space fraction numerator x squared plus 1 over denominator x minus 2 end fraction end cell equals cell fraction numerator limit as x rightwards arrow 1 of space open parentheses x squared plus 1 close parentheses over denominator limit as x rightwards arrow 1 of space open parentheses x minus 2 close parentheses end fraction end cell row blank equals cell fraction numerator 1 squared plus 1 over denominator 1 minus 2 end fraction end cell row blank equals cell fraction numerator 1 plus 1 over denominator negative 1 end fraction end cell row cell limit as x rightwards arrow 1 of space fraction numerator x squared plus 1 over denominator x minus 2 end fraction end cell equals cell negative 2 end cell end table end style$

Jadi, diperoleh $begin mathsize 14px style limit as x rightwards arrow 1 of space fraction numerator x squared plus 1 over denominator x minus 2 end fraction equals negative 2 end style$ .