limit as x approaches infinity of (x^2-25)/(x^2+4x-5)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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lim_{x→ ∞}(x²−25x²+4x−5 )

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Parabola Directrix

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)

Parabola standard equation

4p(x−h)=(y−k)² is the standard equation for a right-left facing parabola with vertex at (h, k),
and a focal length |p|

Rewrite (y−3)²=8(x−5) in the standard form: 4· 2(x−5)=(y−3)²

(h, k)=(5, 3), p=2

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance −p from the center (5, 3) x-coordinate

x=5−p

x=5−2

Refine

x=3

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

limit as x approaches infinity of (x^2-25)/(x^2+4x-5)

Solution

Solution steps

Number Line

Graph

`a`	1
0	2`a`

6	−1
2	3

6	−1
2	3

6	−1
2	3