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