limit (x->0) 1/|x|
the limit doesn't exist.
lim (x-> o+) = + ∞
lim (x-> o-) = - ∞
so limit of the function at the point zero is not existent by definition.
Not true. The function is 1/|x| not 1/x
aah yea you're right. didn't notice the abs function there. anyway, when x approaches zero from left (and right) the function approaches +∞. so the limit is +∞.
that means for all positive deltas and M's if |x - 0| < delta, then f(x) > M. for any large M you like. intuitively you can say: the larger you want M to be, the smaller you need to take delta.
Which still means that there is no limit. Saying "[itex]\lim f(x)= \infty[/itex]" is just a way of saying that the limit does not exist for a particular reason.
well, I think if we're working on extended real number line then it doesn't hurt to say the limit of the function is +∞ because +∞ ∈ R*. and plus the epsilon, delta definition works fine with this example. correct me if i'm wrong.
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