I don't entirely understand your question. By definition,

pointwise if for each fixed x in the domain, the pointwise limit

. For a pointwise limit, you're considering a sequence of points,

where the jth point in your sequence is just

. So for each x and

, we have that

since

(this follows from the square root function being continuous, or a simple epsilon estimate if necessary).

Notice in the definition that the pointwise limit is entirely a local property of a sequence of functions. It does not depend on any other point in the domain. In fact, it's entirely possible for the f_n's to only converge for one point in their domain. By definition, we say that

uniformly if

as

. From the definition, it's clear that a uniform limit implies a pointwise limit. However, the uniform condition is strictly stronger because it's a global condition on the function. All points in the domain must converge to the limiting function at some uniform rate. It does not make sense to as if a sequence of functions converges uniformly at a point.