Pertanyaan

Nilai dari x → ∞ lim x 2 + 1 4 x 5 + x 2 − 2 x − 1 = ....

Nilai dari $x \to \infty lim \frac{4 x ^{5} + x ^{2} - 2 x - 1}{x ^{2} + 1} = ....$

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Nilai .

Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 straight x to the power of 5 plus straight x squared minus 2 straight x minus 1 over denominator straight x squared plus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank infinity end table end style$ .

Pembahasan

Konsep limit tak hingga: metode membagi dengan pangkat tertinggi Diketahui: Pangkat tertinggi adalah , maka pembilang dan penyebut dibagi oleh , maka diperoleh penyelesaiannyasebagai berikut: Jadi, Nilai .

Konsep limit tak hingga: metode membagi dengan pangkat tertinggi

Diketahui: $begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator 4 straight x to the power of 5 plus straight x squared minus 2 straight x minus 1 over denominator straight x squared plus 1 end fraction equals.... end style$

Pangkat tertinggi adalah , maka pembilang dan penyebut dibagi oleh , maka diperoleh penyelesaiannya sebagai berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow infinity of fraction numerator 4 straight x to the power of 5 plus straight x squared minus 2 straight x minus 1 over denominator straight x squared plus 1 end fraction end cell equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style fraction numerator 4 straight x to the power of 5 over denominator straight x to the power of 5 end fraction end style plus begin display style straight x squared over straight x to the power of 5 end style minus begin display style fraction numerator 2 straight x over denominator straight x to the power of 5 end fraction end style minus begin display style 1 over straight x to the power of 5 end style over denominator begin display style straight x squared over straight x to the power of 5 end style plus begin display style 1 over straight x to the power of 5 end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 4 plus 1 over straight x cubed minus 2 over straight x to the power of 4 minus 1 over straight x to the power of 5 end style over denominator begin display style 1 over straight x cubed plus 1 over straight x to the power of 5 end style end fraction end cell row blank equals cell fraction numerator begin display style 4 plus 1 over infinity cubed minus 2 over infinity to the power of 4 minus 1 over infinity to the power of 5 end style over denominator begin display style 1 over infinity cubed plus 1 over infinity to the power of 5 end style end fraction end cell row blank equals cell fraction numerator 4 plus 0 minus 0 minus 0 over denominator 0 plus 0 end fraction end cell row blank equals cell 4 over 0 end cell row blank equals infinity end table end style$

Jadi, Nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 straight x to the power of 5 plus straight x squared minus 2 straight x minus 1 over denominator straight x squared plus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank infinity end table end style$ .