Pertanyaan

x → ∞ lim 6 x 5 − 2 x 3 + 8 x 2 2 x 5 + x 4 − 7 x 3 = ....

$x \to \infty lim \frac{2 x ^{5} + x ^{4} - 7 x ^{3}}{6 x ^{5} - 2 x ^{3} + 8 x ^{2}} = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

$limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction equals 1 third.$

Pembahasan

Ingat: . 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 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction cross times fraction numerator begin display style 1 over x to the power of 5 end style over denominator begin display style 1 over x to the power of 5 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x to the power of 5 over denominator x to the power of 5 end fraction end style plus begin display style x to the power of 4 over x to the power of 5 end style minus begin display style fraction numerator 7 x cubed over denominator x to the power of 5 end fraction end style over denominator begin display style fraction numerator 6 x to the power of 5 over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 2 x cubed over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 8 x squared over denominator x to the power of 5 end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 plus begin display style 1 over x end style minus begin display style 7 over x squared end style over denominator 6 minus begin display style 2 over x squared end style plus begin display style 8 over x cubed end style end fraction end cell row blank equals cell fraction numerator 2 plus begin display style 1 over infinity end style minus begin display style 7 over infinity squared end style over denominator 6 minus begin display style 2 over infinity squared end style plus begin display style 8 over infinity cubed end style end fraction end cell row blank equals cell fraction numerator 2 plus 0 minus 0 over denominator 6 minus 0 plus 0 end fraction end cell row blank equals cell 2 over 6 end cell row blank equals cell 1 third end cell end table$

Jadi $limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction equals 1 third.$