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

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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.

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