Pertanyaan

Nilai limit dari: x → ∞ lim 1 + x 2 x

Nilai limit dari: $x \to \infty lim \frac{x}{1 + x ^{2}}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x over denominator 1 plus straight x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table end style$ .

Pembahasan

Dengan metode pembagian pangkat tertinggi. dari fungsi aljabar di atas, pangkat tertinggi adalah maka pembilang dan penyebut sama-sama dibagi . Sehingga diperoleh: Jadi, nilai dari .

Dengan metode pembagian pangkat tertinggi.

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

dari fungsi aljabar di atas, pangkat tertinggi adalah maka pembilang dan penyebut sama-sama dibagi . Sehingga diperoleh:

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

Jadi, nilai dari $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x over denominator 1 plus straight x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table end style$ .