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limit as x approaches infinity of (x^4-x^2+2)/(x^2(x-1))

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lim_{x→ ∞}(x⁴−x²+2x²(x−1) )

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lim_{x→ ∞}(x⁴−x²+2x²(x−1) )

Apply the following algebraic property: a+b=a(1+ba )
x⁴−x²+2x²(x−1) =x⁴(1−1x² +2x⁴ )x²(x(1−1x ))

=lim_{x→ ∞}(x⁴(1−1x² +2x⁴ )x²x(1−1x ) )

Simplify x⁴(1−1x² +2x⁴ )x²(x(1−1x )) : x(2x⁴ −1x² +1)1−1x

=lim_{x→ ∞}(x(2x⁴ −1x² +1)1−1x )

lim_x→a[f(x)g(x) ]=lim_x→af(x)lim_x→ag(x) , lim_x→ag(x)≠0
With the exception of indeterminate form

=lim_{x→ ∞}(x(2x⁴ −1x² +1))lim_{x→ ∞}(1−1x )

lim_{x→ ∞}(x(2x⁴ −1x² +1))=∞

lim_{x→ ∞}(1−1x )=1

=∞ 1

Apply Infinity Property: ∞c =∞

=∞

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limit as x approaches infinity of (x^4-x^2+2)/(x^2(x-1))

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