Pertanyaan

Nilai dari x → 0 lim x 2 − x ( x 2 − 1 ) ( x 2 − 4 x ) adalah ...

Nilai dari $x \to 0 lim \frac{( x ^{2} - 1 ) ( x ^{2} - 4 x )}{x ^{2} - x}$ adalah ...

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Jawaban terverifikasi

Jawaban

Jawaban yang benar adalah A

Pembahasan

Dengan menerapkan metode pemfaktoran, maka diperoleh: Jadi, Nilai Oleh karena itu, Jawaban yang benar adalah A

Dengan menerapkan metode pemfaktoran, maka diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 0 of fraction numerator left parenthesis straight x squared minus 1 right parenthesis left parenthesis straight x squared minus 4 straight x right parenthesis over denominator straight x squared minus straight x end fraction end cell equals cell limit as straight x rightwards arrow 0 of fraction numerator left parenthesis straight x plus 1 right parenthesis left parenthesis straight x minus 1 right parenthesis times straight x left parenthesis straight x minus 4 right parenthesis over denominator straight x left parenthesis straight x minus 1 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of fraction numerator straight x times left parenthesis straight x plus 1 right parenthesis left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 4 right parenthesis over denominator straight x left parenthesis straight x minus 1 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 0 of left parenthesis straight x plus 1 right parenthesis left parenthesis straight x minus 4 right parenthesis end cell row blank equals cell left parenthesis 0 plus 1 right parenthesis left parenthesis 0 minus 4 right parenthesis end cell row blank equals cell 1 times left parenthesis negative 4 right parenthesis end cell row blank equals cell negative 4 end cell end table end style$

Jadi, Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator left parenthesis straight x squared minus 1 right parenthesis left parenthesis straight x squared minus 4 straight x right parenthesis over denominator straight x squared minus straight x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table end style$

Oleh karena itu, Jawaban yang benar adalah A