x→−2limx2−3x−10x2+6x+8

Pertanyaan

$begin mathsize 14px style limit as x rightwards arrow negative 2 of fraction numerator x squared plus 6 x plus 8 over denominator x squared minus 3 x minus 10 end fraction end style$

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai limit fungsi tersebut adalah $-\frac27$ .

Pembahasan

Dengan menggunakan metode substitusi, kita peroleh limit fungsi yang diberikan berbentuk tak tentu $\frac00$ sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator x squared plus 6 x plus 8 over denominator x squared minus 3 x minus 10 end fraction end cell equals cell fraction numerator open parentheses negative 2 close parentheses squared plus 6 open parentheses negative 2 close parentheses plus 8 over denominator open parentheses negative 2 close parentheses squared minus 3 open parentheses negative 2 close parentheses minus 10 end fraction end cell row blank equals cell fraction numerator 4 minus 12 plus 8 over denominator 4 plus 6 minus 10 end fraction end cell row blank equals cell 0 over 0 end cell end table$

Oleh sebab itu, maka gunakan metode pemfaktoran seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator x squared plus 6 x plus 8 over denominator x squared minus 3 x minus 10 end fraction end cell equals cell limit as x rightwards arrow negative 2 of fraction numerator up diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x plus 4 close parentheses over denominator up diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x minus 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator x plus 4 over denominator x minus 5 end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 close parentheses plus 4 over denominator open parentheses negative 2 close parentheses minus 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator negative 7 end fraction end cell row blank equals cell negative 2 over 7 end cell end table end style$

Dengan demikian, nilai limit fungsi tersebut adalah $-\frac27$ .