Be careful! The limit function is not exactly . Make sure you consider two cases: and .
Also, what do you mean by "unitary convergence"? Do you mean "uniform convergence"?
Note that .
Look for the value of x for which the derivative of (for x positive) is zero and draw the table of variations. Now, find the maximum value of that quantity over th given domain. You have uniform convergence if and only if the limit of the value you get is zero.
hope this helps