Hitunglah nilai Limit berikut! b. x→−1limx2−1x4−1

Pertanyaan

Hitunglah nilai Limit berikut!

b. $limit as x rightwards arrow negative 1 of fraction numerator x to the power of 4 minus 1 over denominator x squared minus 1 end fraction$

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah 2.

Pembahasan

Dengan menggunakan metode pemfaktoran, maka didapatkan:

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

Jadi, nilai limit tersebut adalah 2.

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