Calculus 1 Problem Solving

Welcome to the Calculus 1 problem solving videos. The goal of these videos is to help you understand the basics of problem solving for all of the topics included in the first semester of Calculus or AP Calculus AB. These videos go through selected problems from two textbooks: APEX Calculus (link here) and OpenStax Calculus Volume 1 (link here). Under each topic, there will also be a link to the relevant Khan Academy video series on that topic.


The best way to learn is to try to do the problems yourself, and watch the video on the relevant problem if you're struggling on how to approach it.

If you've found these videos helpful, please let me know. And I do accept donations through PayPal for those who wish to support me. It does help me create more content and maintain these videos and the site.

  1. Limits & Continuity (download problems)

    1. Computing Limits​

    2. Graphical Limits

    3. Limits of Piecewise Functions

    4. Limits with Infinity

    5. Limits with Trig Functions

    6. Continuity

    7. Intermediate Value Theorem

    8. Epsilon-Delta Definition of Limit

  2. Derivatives Practice (download problems)

    1. Using the Definition of the Derivative​

    2. Power Rule

    3. Derivatives of Other Functions

    4. Product Rule & Quotient Rule

    5. Chain Rule

    6. Tangent and Normal Lines

    7. Implicit Differentiation

  3. Applications of Derivatives (download problems)

    1. Absolute and Relative Extrema​

    2. Mean Value Theorem

    3. Concavity and the Second Derivative Test

    4. Related Rates

    5. Optimization

    6. Linear Approximation and Differentials

    7. L'Hospital's Rule

  4. Integration (download problems)

    1. Antiderivatives​

    2. Riemann Sums and the Definition of the Integral

    3. The Definite Integral

    4. Derivatives of Integrals (Fundamental Theorem of Calculus)

    5. U-Substitution

  5. Applications of Integration (download problems)

    1. Average Value​

    2. Area Between Curves

    3. Volumes of Revolution (Washer/Disk method)

    4. Volumes of Revolution (Shell Method)

    5. Volumes using Cross-Sectional Areas

  6. Mixed Applications (download problems)

    1. Interpreting Graphs​

    2. Motion Problems

  7. Differential Equations (download problems)

    1. Verifying Solutions to Differential Equations​

    2. Slope Fields

    3. Separation of Varables


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