Here you find exercises and solutions for real analysis.
Part 1 - Limit of a Sequence
In the Real Analysis course, we have defined the concept of convergence for a real sequence. Let’s assume we already know the convergent sequence that leads to Euler’s number e. Then we can consider similar sequences and calculate the corresponding limits.
Part 2 - Limit of a Sequence II
Part 3 - Limit of a Sequence III
Part 4 - Limit of a Series
Part 5 - Radius of Convergence
Part 6 - Limits of Functions I
Part 7 - Limits of Functions II
Part 8 - Calculate with Logarithms
Part 9 - Logarithm in an Application (DC circuit)
Part 10 - Some Triple-Angle Identity for Sine
Part 11 - Series and Partial Fraction Decomposition
Content of the video:
00:00 Intro
05:55 Comparison Test (n!/n^n)
28:59 Partial Fraction Decomposition and Telescoping
45:48 Comparison Test (1/(4n^2 - 1))
50:21 Comparison Test (harmonic series)
69:30 Partial Fraction Decomposition and Telescoping (again)
Part 12 - Continuous Functions
Other videos related to this topic:
Part 13 - Differentiability and Derivatives I
Part 14 - Differentiability and Derivatives II
Summary of the course Exercises - Real Analysis
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