Solution Guide

1. Derivatives and Limites

1.1 Introduction to the Derivative

1.2 Limits
1.3 The Derivative as a Limit and the Leibniz Notation
1.4 Differentiating Polynomials
1.5 Products and Quotients
1.6 The Linear Approximation and Tangent Lines

2. Sequences and Series

2.2 The Limit of a Sequence
2.3 The Algebraic and Order Limit Theorem
2.4 The Monotone Convergence Theorem and a First Look at Infinite Series
2.5 Subsequences and the Bolzano-Weierstrass Theorem
2.6 The Cauchy Criterion
2.7 Properties of Infinite Sets
2.8 Double Summations and Products of Infinite Series

3. Basic Topology of \(\mathbb{R}\)

3.2 Open and Closed Sets