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Title: Proof of Taylor’s Theorem
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Series: Real Analysis
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Chapter: Differentiable Functions
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YouTube-Title: Real Analysis 47 | Proof of Taylor’s Theorem
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ra47_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Which theorem do we use in the proof of Taylor’s theorem?
A1: Intermediate value theorem
A2: Generalised mean value theorem
A3: L’Hospital’s theorem
A4: Sandwich theorem
Q2: In the proof, we use a telescoping argument for sums. What is the value of the following sum? $$ \sum_{j=1}^n (a_j - a_{j-1})$$
A1: $a_n$
A2: $a_0$
A3: $a_n - a_0$
A4: $a_n - a_{n-1}$
A5: $1$
A6: $-a_n + a_0$
Q3: In the proof, we calculated $f(x_0) - T_n(h)$. What did we get?
A1: $h^{n} \frac{f^{(n+1)}(\xi)}{(n+1)!}$
A2: $h^{n+1} \frac{f^{(n+1)}(\xi)}{(n+1)!}$
A3: $h^{n} \frac{f^{(n)}(\xi)}{n!}$
A4: $h^{n+1} \frac{f^{(n)}(\xi)}{(n+1)!}$
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Last update: 2025-01
