Pertanyaan

Nilai dari x → ∞ lim 3 x 2 + 2021 x 2 + 2 x − 2021 adalah ....

Nilai dari $x \to \infty lim \frac{x ^{2} + 2 x - 2021}{3 x ^{2} + 2021}$ adalah ....

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Habis dalam

Klaim

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 2 x minus 2021 over denominator 3 x squared plus 2021 end fraction end cell end table equals 1 third$ .

Pembahasan

Ingat: Maka diperoleh perhitungan: Jadi .

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0

Maka diperoleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator x squared plus 2 x minus 2021 over denominator 3 x squared plus 2021 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator x squared plus 2 x minus 2021 over denominator 3 x squared plus 2021 end fraction cross times fraction numerator begin display style 1 over x squared end style over denominator begin display style 1 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style x squared over x squared end style plus begin display style fraction numerator 2 x over denominator x squared end fraction end style minus begin display style 2021 over x squared end style over denominator begin display style fraction numerator 3 x squared over denominator x squared end fraction end style plus begin display style 2021 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 1 plus 2 over x minus 2021 over x squared end style over denominator begin display style 3 plus 2021 over x squared end style end fraction end cell row blank equals cell fraction numerator begin display style 1 plus 2 over infinity minus 2021 over infinity squared end style over denominator begin display style 3 plus 2021 over infinity squared end style end fraction end cell row blank equals cell fraction numerator 1 plus 0 plus 0 over denominator 3 plus 0 end fraction end cell row blank equals cell 1 third end cell end table$

Jadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 2 x minus 2021 over denominator 3 x squared plus 2021 end fraction end cell end table equals 1 third$ .