limit as x approaches infinity of (2x+1)/((x+5)^3)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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lim_{x→ ∞}(2x+1(x+5)³ )

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lim_{x→ ∞}(2x+1(x+5)³ )

Apply the following algebraic property: a+b=a(1+ba )
2x+1(x+5)³ =x(2+1x )(x(1+5x ))³

=lim_{x→ ∞}(x(2+1x )(x(1+5x ))³ )

Simplify x(2+1x )(x(1+5x ))³ : 2+1x x²(5x +1)³

=lim_{x→ ∞}(2+1x x²(5x +1)³ )

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→ ∞}(2+1x )lim_{x→ ∞}(x²(5x +1)³)

lim_{x→ ∞}(2+1x )=2

lim_{x→ ∞}(x²(5x +1)³)=∞

=2∞

Apply Infinity Property: c∞ =0

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

limit as x approaches infinity of (2x+1)/((x+5)^3)

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