Assess students' ability to distinguish pointwise and uniform convergence for sequences of real-valued functions on intervals, apply criteria (epsilon-N definitions, uniform Cauchy, Weierstrass M-test), determine when limits may be interchanged with integration or differentiation, prove key results (uniform limits preserve continuity; uniform convergence permits interchange of limit and integral for Riemann integrable functions; sufficient conditions for differentiating termwise), and construct or analyze counterexamples that show failure under mere pointwise convergence.