Further Topics in Mathematics Homework: Limits, Sup, Inf, Norms

This document presents solutions to a mathematics homework assignment focused on several key concepts in mathematical analysis and linear algebra. The assignment addresses the existence of minimum, maximum, infimum, and supremum for a given set, exploring the properties of limits inferior and superior for a sequence. It then delves into vector spaces, calculating the inner product, and various norms (‖𝒙‖1, ‖𝒙‖2, ‖𝒙‖3, ‖𝒙‖∞) of a vector. The solution also addresses the convergence of series, including the alternating harmonic series, and examines uniform convergence of functions. Finally, the assignment covers the calculation of limits for multivariable functions and definite integrals.