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  • 03-02-2020
  • Mathematics
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lim x → ∞ (12x^8-3)/3x^8-2x^7

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LammettHash
LammettHash LammettHash
  • 03-02-2020

Divide through all terms by the highest power of [tex]x[/tex]:

[tex]\dfrac{12x^8-3}{3x^8-2x^7}=\dfrac{12-\frac3{x^8}}{3-\frac2x}[/tex]

As [tex]x\to\infty[/tex], the terms with [tex]x[/tex] in the denominator will vanish, leaving us with

[tex]\displaystyle\lim_{x\to\infty}\frac{12x^8-3}{3x^8-2x^7}=\frac{12}3=4[/tex]

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