Pertanyaan

x → − 1 lim x 2 + 4 x + 3 x 2 − 1 = ...

$x \to - 1 lim \frac{x ^{2} - 1}{x ^{2} + 4 x + 3} =$ ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Dengan menggunakan metode pemfaktoran, diperoleh: Maka, hasil dari .

Dengan menggunakan metode pemfaktoran, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 1 of space fraction numerator x squared minus 1 over denominator x squared plus 4 x plus 3 end fraction end cell equals cell limit as x rightwards arrow negative 1 of space fraction numerator x squared minus x plus x minus 1 over denominator x squared plus 3 x plus x plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of space fraction numerator x open parentheses x minus 1 close parentheses plus 1 open parentheses x minus 1 close parentheses over denominator x open parentheses x plus 3 close parentheses plus 1 open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator down diagonal strike open parentheses x plus 1 close parentheses end strike open parentheses x minus 1 close parentheses over denominator down diagonal strike open parentheses x plus 1 close parentheses end strike open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator x minus 1 over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator negative 1 minus 1 over denominator negative 1 plus 3 end fraction end cell row blank equals cell fraction numerator negative 2 over denominator 2 end fraction end cell row blank equals cell negative 1 end cell end table$

Maka, hasil dari $limit as x rightwards arrow negative 1 of space fraction numerator x squared minus 1 over denominator x squared plus 4 x plus 3 end fraction equals negative 1$ .