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limit as x approaches infinity of ((x^3-21x))/((5+4x-x^2))

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lim_{x→ ∞}((x³−21x)(5+4x−x²) )

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−∞

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lim_{x→ ∞}(x³−21x5+4x−x² )

Divide by highest denominator power: x−21x 5x² +4x −1

=lim_{x→ ∞}(x−21x 5x² +4x −1 )

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−21x )lim_{x→ ∞}(5x² +4x −1)

lim_{x→ ∞}(x−21x )=∞

lim_{x→ ∞}(5x² +4x −1)=−1

=∞ −1

Apply Infinity Property: ∞−c =−∞

=−∞

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

limit as x approaches infinity of ((x^3-21x))/((5+4x-x^2))

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