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Title: Application for 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 46 | Application for Taylor’s Theorem
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Bright video: https://youtu.be/qmxY1DKx-vA
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Dark video: https://youtu.be/7tgCjjvrZSE
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): https://youtu.be/zRoyHrMNOO8
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Original video for YT-Members (dark): https://youtu.be/fnI_JAVsMpQ
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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: ra46_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Consider the logarithm function. What is the $n$-th derivative of $\log$?
A1: $\frac{1}{x}$
A2: $\frac{1}{x^n}$
A3: $\frac{n!}{x^n}$
A4: $(-1)^{n-1} \frac{(n-1)!}{x^n}$
A5: $-\frac{(n-1)!}{x^n}$
Q2: Let $f \colon \mathbb{R} \rightarrow \mathbb{R}$ be 3-times differentiable. Let $T_2(h)$ be the $2$nd order Taylor polynomial with expansion point $x_0 = 0$. What do we get when we calculate $f(0.2) - T_2(0.2)$?
A1: $R_2(0)$
A2: $R_3(0)$
A3: $R_2(0.2)$
A4: $f(0.2)$
A5: $f(0.5)$
A6: $f(0)$
Q3: Let $f \colon \mathbb{R} \rightarrow \mathbb{R}$ be 3-times differentiable. Let $T_2(h)$ be the $2$nd order Taylor polynomial with expansion point $x_0 = 0$. How can we show how good the approximation $T_2(0.2)$ for the value $f(0.2)$ is?
A1: We calculate $R_2(0)$.
A2: We find bounds for the number $R_2(0.2)$ by going through all intermediate points $\xi$.
A3: We calculate $T_2(0.2)$.
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Last update: 2025-01
