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APEX Calculus - Limits

Sean Fitzpatrick via YouTube

Overview

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This course on Limits in Calculus aims to help learners understand the concept of limits and their applications. By the end of the course, students will be able to identify different types of limits, work with difference quotients, analyze functions for continuity, and evaluate limits at infinity. The course covers topics such as basic properties of limits, one-sided limits, continuity, and limits at infinity. The teaching method includes theoretical explanations, examples, and problem-solving sessions. This course is intended for individuals interested in building a strong foundation in calculus and preparing for more advanced topics in mathematics.

Syllabus

Limits: Introduction - 01. Calculus Overview.
Limits: Introduction - 02. Concept of the Limit.
Limits: Introduction - 03. sin(x) over x.
Limits: Introduction - 04. Rational function, graphically.
Limits: Introduction - 05. a Piecewise Function.
Limits: Introduction - 06. Ways a limit fails to exist.
Limits: Introduction - 07. Jumps and Aysmptotes.
Limits: Introduction - 08. Oscillation.
Limits: Introduction - 09. Difference Quotients.
Limits: Introduction - 10. Difference quotient example.
Limits: Introduction - 11. Difference Quotient, with simplifying.
Limits: Definition - 01. Informal.
Limits: Definition - 02. Precise.
Limits: Definition - 03. Square Root; trying epsilon = 1.
Limits: Definition - 04. Square Root; general epsilon.
Limits: Definition - 05. Quadratic.
Limits: Definition - 06. Polynomial.
Limits: Analytic - 01. Basic Properties.
Limits: Analytic - 02. Sum Rule.
Limits: Analytic - 03. Properties.
Limits: Analytic - 04. Using Properties.
Limits: Analytic - 05. Two Important Theorems.
Limits: Analytic - 06. Algebraic, Example 1.
Limits: Analytic - 07. Algebraic, Example 2.
Limits: Analytic - 08. Squeeze Theorem.
Limits: Analytic - 09. Limit of sine at zero.
Limits: Analytic - 10. Sine limits can be done by direct substitution.
Limits: Analytic - 11. sin(x) over x.
Limits: Analytic - 12. Trig Limits.
Limits: One-sided - 01. Definition.
Limits: One-sided - 02. Example 1.
Limits: One-sided - 03. Example 2.
Limits: One-sided - 04. Example 3.
Limits: One-sided - 05. Example 4.
Limits: Continuity - 01. Definition.
Limits: Continuity - 02. Basic Examples.
Limit: Continuity - 03. Properties.
Limits: Continuity - 04. Using properties.
Limits: Continuity - 05. Intervals of continuity.
Limits: Continuity - 06. Intervals, again.
Limits: Continuity - 07. Types of Discontinuity.
Limits: Continuity - 08. IVT - statement.
Limits: Continuity - 09. IVT - example.
Limits: Continuity - 10. IVT - bisection.
Limits: Infinite - 01. Definition.
Limits: Infinite - 02. Example using definition.
Limits: Infinite - 03. Example with 1/x.
Limits: Infinite - 04. Vertical Asymptotes.
Limits: Infinite - 05. Vertical Asymptote Example.
Limits: At Infinity - 01. Definition.
Limits: At Infinity - 02. Example using definition.
Limits: At Infinity - 03. Basic Examples.
Limits: At Infinity - 04. Rational Function Example.
Limits: At Infinity - 05. Example with Radical.

Taught by

Sean Fitzpatrick

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