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## Main Question or Discussion Point

In the case of a function like [itex]\sqrt{x}[/itex], where the function is only defined for values equal or greater than 0, does the limit exist at 0? I know both the left and right side limits as x approaches a must be equivalent and real for the limit at a to exist, but what if the domain is restricted? Do we consider the function differently when it is on a restricted domain? Would the limit for the above exist, and equal 0, as x approaches 0?

Sorry if this question has been asked already. I just keep reading contradictory statements online, and that it does exist only if you consider complex numbers (I am not, in this case). Any light shed on the topic would be greatly appreciated. Thanks!

Sorry if this question has been asked already. I just keep reading contradictory statements online, and that it does exist only if you consider complex numbers (I am not, in this case). Any light shed on the topic would be greatly appreciated. Thanks!