Pertanyaan

Tentukan nilai limit dari: a. x → ∞ lim 4 x 2 − 6 x + 1 3 x 3 + 5 x 2 − 2 (cara biasa)

Tentukan nilai limit dari:

a. $x \to \infty lim \frac{3 x ^{3} + 5 x ^{2} - 2}{4 x ^{2} - 6 x + 1}$ (cara biasa)

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Jawaban terverifikasi

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$begin mathsize 14px style limit as x rightwards arrow infinity of table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x cubed plus 5 x squared minus 2 over denominator 4 x squared minus 6 x plus 1 end fraction end cell end table equals infinity end style$ .

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 3 x cubed plus 5 x squared minus 2 over denominator 4 x squared minus 6 x plus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator up diagonal strike x cubed end strike x open parentheses 3 plus begin display style 5 over x end style minus begin display style 2 over x cubed end style close parentheses over denominator up diagonal strike x squared end strike open parentheses 4 minus begin display style 6 over x end style plus begin display style 1 over x squared end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x open parentheses 3 plus begin display style 5 over x end style minus begin display style 2 over x cubed end style close parentheses over denominator 4 minus begin display style 6 over x end style plus begin display style 1 over x squared end style end fraction end cell row blank equals cell fraction numerator infinity open parentheses 3 plus 0 minus 0 close parentheses over denominator 4 minus 0 plus 0 end fraction end cell row blank equals cell infinity over 4 end cell row blank equals infinity end table end style$

Dengan demikian, $begin mathsize 14px style limit as x rightwards arrow infinity of table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x cubed plus 5 x squared minus 2 over denominator 4 x squared minus 6 x plus 1 end fraction end cell end table equals infinity end style$ .