Assess undergraduate students' ability to analyze and distinguish pointwise and uniform convergence for sequences of functions on a closed interval [a,b]. Tasks should require precise ε-N and uniform ε-N arguments, use of the sup-norm and Weierstrass M-test, construction of proofs or counterexamples for given sequences, and discussion of consequences for continuity, integration, and differentiation of limits. Include at least one sequence that is pointwise but not uniformly convergent and ask for rigorous justification.