Appendix C Theory and procedures
2 Limits: informal definition
Theorem 2.12 Constant and identity functions
Theorem 2.13 Limit rules
Corollary 2.17 Evaluation (polynomials and rational functions)
3 Limits: algebraic technique and sandwich theorem
Theorem 3.4 Sandwich theorem
Procedure 3.5 Sandwich theorem
Theorem 3.11 Limits and absolute value
Theorem 3.12 Sine and cosine evaluation at zero
4 Limits: formal definition
Procedure 4.4 Epsilon-delta proof for limits
Theorem 4.11 Inequality rules
5 One-sided limits
Theorem 5.6 One-sided limits test
Theorem 5.8 Classic trig limits
6 Continuity: definition
Theorem 6.10 Continuous functions
Theorem 6.11 Continuity rules
Theorem 6.12 Continuity composition rule
7 Continuity: intermediate value theorem
Theorem 7.3 Intermediate value theorem (IVT)
8 Limits at infinity
Theorem 8.9 Limit at infinity: reciprocal power functions
9 Infinite limits
Theorem 9.7 Power functions and their reciprocals
Theorem 9.8 Infinite limit formulas
Theorem 9.11 Limit at infinity: rational functions
11 Derivative: function
Theorem 11.9 Differentiable implies continuous
12 Derivative: rules
Theorem 12.1 Derivative formulas: constant and power functions
Theorem 12.4 Derivative rules
Theorem 12.8 Derivative: polynomials
13 Derivative as rate of change
Procedure 13.1 Rate of change interpretations
14 Derivative: trig functions
Theorem 14.1 Derivative formulas: sine and cosine
Theorem 14.4 Derivative formulas: trig functions
15 Chain rule
Theorem 15.1 Chain rule
Procedure 15.2 Chain rule
16 Implicit differentiation
Procedure 16.4 Implicit differentiation
17 Related rates I
Procedure 17.4 Related rates
19 Linearization
Procedure 19.7 Linear approximation
20 Extreme value theorem
Theorem 20.1 Extreme value theorem
Theorem 20.11 Critical points and extreme values
Procedure 20.13 Extreme value theorem
21 Mean value theorem
Theorem 21.1 Rolle’s theorem
Theorem 21.3 Mean value theorem (MVT)
Corollary 21.5 Constant function characterization
Corollary 21.6 Functions with identical derivatives
Corollary 21.10 Taylor’s theorem (\(k=1\))
22 Monotonicity and first derivative test
Theorem 22.2 Derivative and monotonicity
Procedure 22.5 Intervals of monotonicity
Theorem 22.6 First derivative test
Procedure 22.7 Classify critical points: first derivative test
23 Concavity and inflection points
Procedure 23.7 Concavity and inflection points
Theorem 23.10 Second derivative test
24 Curve sketching I
Procedure 24.1 Curve sketching
26 Applied optimization
Procedure 26.4 Applied optimization
Procedure 26.7 Generalized extreme value theorem
