F.6 MATHS & STATS.. Asymptotes

To find find horizontal asymptote(s)
Consider x→+∞ and x→-∞
when x→+∞
lim(x→+∞ )e^-x^2
=lim(x→+∞ ) 1/e^(x^2)
=0
Similarly
lim(x→-∞ )e^-x^2
=0
So the horizontal asymptote is y=0
For vertical asymptote.
Notice that since when x=0, y=e^-x^2=e^0=1
So, there is no vertical asymptote


2007-04-07 05:28:40 補充：
you can see the graph at herehttp://in.geocities.com/myisland8132/7007040700419.JPG

2007-04-07 05:40:49 補充：
Sorry I say something wrongFor vertical asymptote, its definition isLine of the form x = a, where a is a constant, for which f(x)->∞ or f(x)->-∞ as x->a

2007-04-07 05:41:07 補充：
Now, because y is a continuous function, so there does not exist x = a such that f(x)->∞ or f(x)->-∞ as x->aShow that there is no vertical asymptote你一定要答continuous function才成