It's known that limx→x0f(x)=A, how to prove limx→x03√f(x)=3√A?
Here's what I've got now:
When A=0, to prove limx→x03√f(x)=0: Since we have limx→x0f(x)=A=0, so |f(x)|<ϵ. => |3√f(x)|<ϵ30<ϵ
When A≠0, |3√f(x)−3√A|=|f(x)−A||f(x)23+(f(x)A)13+A23|...
How can I deal with (f(x)A)13? Thanks.
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