Exercises - Real Analysis

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.


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Part 2 - Limit of a Sequence II


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Part 3 - Limit of a Sequence III


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Part 4 - Limit of a Series


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Part 5 - Radius of Convergence


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Part 6 - Limits of Functions I


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Part 7 - Limits of Functions II


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Part 8 - Calculate with Logarithms


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Part 9 - Logarithm in an Application (DC circuit)


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Part 10 - Some Triple-Angle Identity for Sine


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Part 11 - Series and Partial Fraction Decomposition


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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


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Part 13 - Differentiability and Derivatives I


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Part 14 - Differentiability and Derivatives II


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Summary of the course Exercises - Real Analysis


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