Assess students' understanding of uniform versus pointwise convergence for sequences of real-valued functions on subsets of R, including definitions, key theorems, and typical hypotheses that guarantee preservation of continuity, Riemann/Lebesgue integrability, and differentiability. Expect short proofs, verification of hypotheses (e.g., uniform convergence of derivatives and convergence at a point), construction or analysis of counterexamples, and application of results to interchange limits with integrals and derivatives on closed intervals.