Assess students' ability to distinguish pointwise and uniform convergence for sequences of real-valued functions on intervals; apply definitions and tests (ε-N, uniform Cauchy, Weierstrass M-test) to determine convergence; analyze consequences for preservation of continuity and integrability, justify term-by-term integration under uniform convergence, state and apply sufficient conditions for term-by-term differentiation (e.g., uniform convergence of derivatives plus convergence at a point), and construct or identify counterexamples where mere pointwise convergence fails to permit interchange of limit with integral or derivative.