real analysis paper

1. In about one page, discuss the theme "Analysis is all about approximation." Be sure to address the following five important calculus topics and any connection to approximation: Differentiability Integrability Convergence of Infinite Series Taylor Polynomials Uniform Continuity Also address at least one of the following important calculus topics and any connection to approximation: Density of Rationals in R. Least Upper Bound Sequence Convergence and Divergence Limits of functions Continuity 2. Other than Approximation, what is the most important definition, axiom, theorem, or concept in all of Real Analysis? Justify your response in an essay that is approximately one page long.