Pertanyaan

x → ∞ lim 2 x 4 + x 2 + 3 x − 1 x 4 + x 3 − 5 = ...

$x \to \infty lim \frac{x ^{4} + x ^{3} - 5}{2 x ^{4} + x ^{2} + 3 x - 1} = ...$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Mencari hasil limit tak hingga: Jadi, . Dengan demikian, jawaban yang tepat adalah D.

Mencari hasil limit tak hingga:

$limit as x rightwards arrow infinity thin space of fraction numerator x to the power of 4 plus x cubed minus 5 over denominator 2 x to the power of 4 plus x squared plus 3 x minus 1 end fraction equals limit as x rightwards arrow infinity thin space of fraction numerator x to the power of 4 plus x cubed minus 5 over denominator 2 x to the power of 4 plus x squared plus 3 x minus 1 end fraction. fraction numerator begin display style 1 over x to the power of 4 end style over denominator begin display style 1 over x to the power of 4 end style end fraction equals limit as x rightwards arrow infinity thin space of fraction numerator 1 plus 1 over x minus 5 over x to the power of 4 over denominator 2 plus 1 over x squared plus 3 over x cubed minus 1 over x to the power of 4 end fraction equals fraction numerator 1 plus 0 minus 0 over denominator 2 plus 0 plus 0 minus 0 end fraction equals 1 half$

Jadi, $limit as x rightwards arrow infinity thin space of open parentheses fraction numerator x to the power of 4 plus x cubed minus 5 over denominator 2 x to the power of 4 plus x squared plus 3 x minus 1 end fraction close parentheses equals 1 half$ .

Dengan demikian, jawaban yang tepat adalah D.