How to determine whether a sequence of $\mathbb{R}$ functions converges uniformly or pointwise to a function? Although I know the definition, I don't fully understand how to use it. Does this correlate to the derivative of a function? I.e., my thinking is along the lines of, if a function grows two quickly, limsup of the error, as n->inf, on all of the domain won't be 0. To understand this concept, is to be able to come up with functions satisfying the required domain and convergence criteria. Therefore, if you could do such an example it would probably help me understand. For example, how do I determine the type of convergence of $lim_{n\rightarrow\infty} x^n=0$ on the interval [0,1)?
How to determine whether a sequence of functions converges uniformly or pointwise to a function?
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calculus