lim g(x) = lim h(x) - lim f(x)
because the "limit" operation distributes over addition/subtraction. <-- Are you allowed to assume this in your problem or do you essentially have to prove this?
If RHS is finite then LHS is finite. QED.
I have that the limit of f(x) as x goes to c exists and that the limit of g(x) as x goes to c does not exist.
How do I prove that the limit of h(x) as x goes to c does not exist (where h = f + g)?
What can you say about the limit of g using epsilon notation to reach a contradiction?
lim g(x) = lim h(x) - lim f(x)
because the "limit" operation distributes over addition/subtraction. <-- Are you allowed to assume this in your problem or do you essentially have to prove this?
If RHS is finite then LHS is finite. QED.
i guess that could work.
you have for all and all those 's and stuff that
but , where
where and are the limits of and respectfully.
had existed, we would have , where is the limit of
but,
i don't really like this though. hwhelper's way is perhaps better. maybe you can fix it up