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Question
Find the asymptotes of the following curves:
f(x) = `(x^2 - 6x - 1)/(x + 3)`
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Solution
When x = – 3, the function becomes undefined.
∴ x = – 3 is the vertical asymptote.
No Horizontal asymptote exist for the curve.
Oblique asymptote can be obtained by polynomial long division method
`x - 9`
`x + 3")"overline(x^2 - 6x - 1)`
`x^2 + 3x`
(–) (–)
`- 9x - 1`
`- 9x - 27`
(+) (+)
26
∴ y = x – 9 is the slant or oblique asymptote.
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