Suppose f is real. Prove if L = lim f(x) (x goes to a) exists, then abs f(x) goes to abs L, as x goes to a.
Show that there is a funciton such that as x goes to a, abs f(x) goes to abs L, but the limit of f(x) does not exist.
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One of the most useful properties of absolute value is this: .
It is also one of the least known/taught.
Using the definition for limit with the above, you problem ‘falls’ into your lap.
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