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# asymptotes question watch

1. y = [(x-1)(x+4)]/(x^2 + 4)

write down the equation of the asymptote parallel to the x axis

i started by seeing what happened to the graph as x tends to plus and minus infinity. I thought that to minus infinity y would tend to zero and to plus infinity i wasnt quite sure but thought it might be 1. Can u help pls?
2. To both +ve and -ve infinity it would tend to y=1
3. ne1? Im really unsure cos it seems that for x = + infinity, y would end up a top heavy fraction. Please help sum1?

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so i just ignore the 3x on top cos it is much smaller than infinity squared. Cool thanx.
4. (Original post by ryan750)
so i just ignore the 3x on top cos it is much smaller than infinity squared. Cool thanx.
Yeah, if you ever want to double-check an asymptote just consider x= ±1000000 or something.
5. y = [(x-1)(x+4)]/(x² + 4)
=(x²+3x-4)/(x²+4)
=(1+3/x-4/x²)/(1+4/x²)

but we know 3/x and 4/x²-->0 as x-->∞

so y-->1/1=1

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