A calculus problem by Star Fall
How many of the following statement(s) is/are wrong?
- The pointwise limit of a sequence of continuous functions is continuous.
- Every continuous function defined on closed real intervals is Riemann integrable.
- Real power series are uniformly convergent within compact subintervals of their interval of convergence.
- Every real-valued smooth (infinitely differentiable) function admits a Maclaurin series expansion which converges to the function on some open subset of its domain.
- A convergent series whose terms are differentiable functions of x can always be differentiated termwise to obtain the derivative of the limit function.