Pertanyaan

Hitunglah limit fungsi berikut. x → ∞ lim 10 x 3 + 5 x 3 x 2 + 5 x − 7

Hitunglah limit fungsi berikut.

$x \to \infty lim \frac{3 x ^{2} + 5 x - 7}{10 x ^{3} + 5 x}$

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Jawaban terverifikasi

Jawaban

nilai limit di atas adalah 0.

Pembahasan

Jadi, nilai limit di atas adalah 0.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 3 x squared plus 5 x minus 7 over denominator 10 x cubed plus 5 x end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator x cubed open parentheses begin display style 3 over x end style plus begin display style 5 over x squared end style minus begin display style 7 over x cubed end style close parentheses over denominator x cubed open parentheses 10 plus begin display style 5 over x squared end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 3 over x end style plus begin display style 5 over x squared end style minus begin display style 7 over x cubed end style over denominator 10 plus begin display style 5 over x squared end style end fraction end cell row blank equals cell fraction numerator 0 plus 0 minus 0 over denominator 10 plus 0 end fraction end cell row blank equals cell 0 over 10 end cell row blank equals 0 end table end style$

Jadi, nilai limit di atas adalah 0.