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Quantum Engineering Year 0: Mathematical Foundations Month 1Day 5

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Year 0·Month 1·Week 1

Day 5: Week 1 Problem Set — Limits and Continuity

Day 5 of 2,016~8 min read

Learning Objectives

•Confidently evaluate any standard limit
•Write clean ε-δ proofs
•Analyze continuity of any given function
•Apply IVT effectively
•Identify your remaining weak areas

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Instructions Section A Limit Evaluation 4 points each A1 Direct Substitution A2 Factoring 00 form A3 Factoring with Quadratics A4 Rationalizing Numerator A5 Rationalizing Denominator A6 Complex Fraction A7 Trigonometric use known limits A8 Trigonometric A9 Limit at Infinity A10 Limit at Infinity Different Degrees Section B One-Sided Limits 5 points each B1 Piecewise Function B2 Absolute Value B3 Vertical Asymptote Section C Squeeze Theorem 6 points each C1 Classic Application C2 Bounded Oscillation C3 Limit at Infinity Section D Epsilon-Delta Proofs 8 points each D1 Linear Function D2 Quadratic Function D3 Rational Function D4 Challenge Section E Continuity Analysis 5 points each E1 Find All Discontinuities E2 Making Functions Continuous E3 Two Constants E4 Continuity from Definition Section F IVT Applications 7 points each F1 Existence of Roots F2 Fixed Point F3 Physical Application F4 Narrowing a Root Section G Conceptual Questions 4 points each G1 True or False with justification G2 Counterexample Construction G3 Limit Does Not Exist Section A Answers Section B Answers Section C Answers Section D Answers Section E Answers Section F Answers Section G Answers Self-Assessment Scoring Grade Scale Reflection Weekend Plan

Day 4Day 5 of 2,016Day 6