Exercises

Exercise sheets with worked solutions, organized as the parts of the notes. Try each exercise on your own first: the solution opens with a click.

• Numbers and logic

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  • Maxima, minima, suprema and infima · 11 exercises
  • Equations and inequalities in one real variable · 14 exercises
  • Summations · 2 exercises
  • Principle of mathematical induction · 5 exercises
  • Complex numbers · 21 exercises

• Functions

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  • Domains of functions · 4 exercises
  • Inverse functions · 11 exercises

• Limits of sequences

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  • Properties of sequences · 4 exercises
  • Verifying limits of sequences · 6 exercises
  • Computing limits of sequences · 35 exercises
  • Additional exercises · 17 exercises

• Limits of functions

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  • Limits of real functions of a real variable · 39 exercises

• Derivatives

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  • Cusps, inflection points and tangents · 4 exercises
  • Computing derivative functions · 27 exercises
  • Tangent lines · 8 exercises
  • Asymptotes · 3 exercises
  • Continuous extensions · 4 exercises
  • Differentiability · 7 exercises
  • Parametric equations · 1 exercises
  • Curve sketching · 11 exercises
  • Maclaurin expansions · 3 exercises
  • Limits via asymptotic expansions · 1 exercises
  • Newton's method · 1 exercises
  • Bisection method · 4 exercises
  • Finding local and global extrema and extremum points · 4 exercises

• Series

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  • Numerical series · 29 exercises

• Integrals

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  • Antiderivatives · 6 exercises
  • Integrals · 20 exercises