Pertanyaan

x → ∞ lim 3 x 4 + x 3 + 5 4 x 2 − 8 x + 1 = ...

$x \to \infty lim \frac{4 x ^{2} - 8 x + 1}{3 x ^{4} + x ^{3} + 5} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

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Pembahasan

Ingat bahwa: Sehingga, Jadi, .

Ingat bahwa:

$limit as x rightwards arrow a of open square brackets fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction close square brackets equals fraction numerator lim subscript x rightwards arrow a end subscript f open parentheses x close parentheses over denominator lim subscript x rightwards arrow a end subscript g open parentheses x close parentheses end fraction comma thin space limit as x rightwards arrow a of g open parentheses x close parentheses not equal to 0$

Sehingga,

$limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 4 x squared minus 8 x plus 1 over denominator square root of 3 x to the power of 4 plus x cubed plus 5 end root end fraction close parentheses equals limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 4 minus 8 over x plus 1 over x squared over denominator square root of 3 plus 1 over x plus 5 over x to the power of 4 end root end fraction close parentheses equals fraction numerator lim subscript x rightwards arrow infinity thin space end subscript open parentheses 4 minus 8 over x plus 1 over x squared close parentheses over denominator lim subscript x rightwards arrow infinity thin space end subscript open parentheses square root of 3 plus 1 over x plus 5 over x to the power of 4 end root close parentheses end fraction equals fraction numerator open parentheses 4 minus 8 over infinity plus 1 over infinity squared close parentheses over denominator open parentheses square root of 3 plus 1 over infinity plus 5 over infinity to the power of 4 end root close parentheses end fraction equals fraction numerator 4 over denominator square root of 3 end fraction equals fraction numerator 4 square root of 3 over denominator 3 end fraction$

Jadi, $limit as x rightwards arrow infinity thin space of open parentheses fraction numerator 4 x squared minus 8 x plus 1 over denominator square root of 3 x to the power of 4 plus x cubed plus 5 end root end fraction close parentheses equals fraction numerator 4 square root of 3 over denominator 3 end fraction$ .