Pertanyaan

Nilai dari lim x → ∞ ( x 2 − 1 ) ( 12 x − 2 ) ( 4 x 2 − 2 ) ( x 2 − 2 x + 1 ) adalah ...

Nilai dari $lim_{x \to \infty} \frac{( 4 x ^{2} - 2 ) ( x ^{2} - 2 x + 1 )}{( x ^{2} - 1 ) ( 12 x - 2 )}$ adalah ...

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Limit Tak Hingga Fungsi Aljabar Keterangan: Diketahui ,maka: Perhatikan pangkat tertinggi pembilang dan penyebut. Karena , maka: Jadi, jawaban yang tepat adalah A.

Limit Tak Hingga Fungsi Aljabar

$table attributes columnalign right center left columnspacing 0px end attributes row cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below fraction numerator size 12px a subscript size 12px n size 12px x to the power of size 12px n size 12px plus size 12px a subscript size 12px n size 12px minus size 12px 1 end subscript size 12px x to the power of size 12px n size 12px minus size 12px 1 end exponent size 12px plus size 12px a subscript size 12px n size 12px minus size 12px 2 end subscript size 12px x to the power of size 12px n size 12px minus size 12px 2 end exponent size 12px plus size 12px. size 12px. size 12px. over denominator size 12px p subscript size 12px m size 12px x to the power of size 12px m size 12px plus size 12px p subscript size 12px m size 12px minus size 12px 1 end subscript size 12px x to the power of size 12px m size 12px minus size 12px 1 end exponent size 12px plus size 12px p subscript size 12px m size 12px minus size 12px 2 end subscript size 12px x to the power of size 12px m size 12px minus size 12px 2 end exponent size 12px plus size 12px. size 12px. size 12px. end fraction end cell size 12px equals size 12px L row size 12px L size 12px equals cell begin mathsize 12px style open curly brackets table attributes columnalign left end attributes row cell L equals 0 comma space n less than m end cell row cell table row cell L equals a subscript n over p subscript m comma space n equals m end cell row cell L equals infinity comma space n greater than m end cell end table end cell end table close end style end cell end table$

Keterangan:

Diketahui $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 4 x squared minus 2 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses over denominator left parenthesis x squared minus 1 right parenthesis open parentheses 12 x minus 2 close parentheses end fraction end cell end table$ , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x squared minus 2 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses over denominator left parenthesis x squared minus 1 right parenthesis open parentheses 12 x minus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 4 minus 8 x cubed plus 2 x squared plus 4 x minus 2 over denominator 12 x cubed minus 2 x squared minus 12 x plus 2 end fraction end cell end table$

Perhatikan pangkat tertinggi pembilang dan penyebut.

Karena n equals 4 comma space m equals 3 rightwards arrow n greater than m , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 4 x squared minus 2 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses over denominator left parenthesis x squared minus 1 right parenthesis open parentheses 12 x minus 2 close parentheses end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank infinity end table$

Jadi, jawaban yang tepat adalah A.