Pertanyaan

Nilai dari x → ∞ lim x − 1 x 2 adalah ....

Nilai dari $x \to \infty lim \frac{x ^{2}}{x - 1}$ adalah ....

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Klaim

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa Perhatikan bahwa apabila nilai x semakin besar menuju tak hingga, maka nilai x ditambah 1 juga akan menuju tak hingga. Oleh karena itu, Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight infinity of invisible function application fraction numerator x squared over denominator x minus 1 end fraction end cell equals cell limit as x rightwards arrow straight infinity of invisible function application fraction numerator x squared minus x plus x over denominator x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator x squared minus x over denominator x minus 1 end fraction plus fraction numerator x over denominator x minus 1 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application fraction numerator x squared minus x over denominator x minus 1 end fraction plus limit as x rightwards arrow straight infinity of invisible function application fraction numerator x over denominator x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application fraction numerator x up diagonal strike open parentheses x minus 1 close parentheses end strike over denominator up diagonal strike x minus 1 end strike end fraction plus limit as x rightwards arrow straight infinity of invisible function application fraction numerator x over denominator x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application x plus limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator x over denominator x minus 1 end fraction times fraction numerator 1 over x over denominator 1 over x end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application x plus limit as x rightwards arrow straight infinity of invisible function application fraction numerator 1 over denominator 1 minus 1 over x end fraction end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application x plus fraction numerator 1 over denominator 1 minus 0 end fraction end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application x plus 1 end cell row blank blank blank end table end style$

Perhatikan bahwa apabila nilai x semakin besar menuju tak hingga, maka nilai x ditambah 1 juga akan menuju tak hingga. Oleh karena itu,

$begin mathsize 14px style limit as x rightwards arrow straight infinity of invisible function application fraction numerator x squared over denominator x minus 1 end fraction equals limit as x rightwards arrow straight infinity of invisible function application x plus 1 equals infinity end style$

Jadi, jawaban yang tepat adalah A.