# A calculus problem by Star Fall

Calculus Level 5

How many of the following statement(s) is/are wrong?

1. The pointwise limit of a sequence of continuous functions is continuous.
2. Every continuous function defined on closed real intervals is Riemann integrable.
3. Real power series are uniformly convergent within compact subintervals of their interval of convergence.
4. Every real-valued smooth (infinitely differentiable) function admits a Maclaurin series expansion which converges to the function on some open subset of its domain.
5. A convergent series whose terms are differentiable functions of x can always be differentiated termwise to obtain the derivative of the limit function.
×