Activity for TextKit
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #288129 | Initial revision | — | over 1 year ago |
| Question | — |
Which other Real Analysis textbooks unusually recommend ending delta-epsilon proofs with a cluttered, bedecked $\epsilon$? 1. Most textbooks conclude $\delta-\epsilon$ proofs tidily with $\epsilon > 0$ alone, as in red beneath. But what's the official term for this alternative $\delta-\epsilon$ proof, as in green beneath? 2. I forgot the particulars of another textbook that I read, not the one quoted below. It advise... (more) |
— | over 1 year ago |
| Edit | Post #287647 |
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— | almost 2 years ago |
| Edit | Post #287647 | Initial revision | — | almost 2 years ago |
| Answer | — |
A: Expanding the Integration problem. This is just middle school algebra. $\frac{1}{b-a} \left[ -\dfrac{1}{2}(a + b){\color{red}{(b^2 - a^2)}} + \dfrac{1}{4}(b+ a)^2(b-a)\right] \equiv \frac{1}{b-a} \left[ -\dfrac{1}{2}(a + b){\color{red}{(a + b)(b - a)}} + \dfrac{1}{4}(b+ a)^2(b-a)\right] \equiv \frac{1}{b-a} \left[ -\dfrac{1}{2}{\c... (more) |
— | almost 2 years ago |
| Comment | Post #287625 |
@#53398 I recast my post. Better now? (more) |
— | almost 2 years ago |
| Edit | Post #287625 |
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— | almost 2 years ago |
| Edit | Post #287625 |
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— | almost 2 years ago |
| Edit | Post #287625 |
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— | almost 2 years ago |
| Edit | Post #287625 |
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— | almost 2 years ago |
| Edit | Post #287625 |
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— | almost 2 years ago |
| Edit | Post #287625 |
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— | almost 2 years ago |
| Edit | Post #287625 | Initial revision | — | almost 2 years ago |
| Question | — |
What did James Stewart mean by "the line integral reduces to an ordinary single integral in this case" ? 1. Please see the question in the title, in reference to the paragraph beside my two green question marks in the image below. 1. How do you symbolize "the line integral reduces to an ordinary single integral in this case"? $\int^ba f(x {\color{goldenrod}{, 0)}} \, dx = \int^ba f(x) \, dx $? 1. F... (more) |
— | almost 2 years ago |
| Edit | Post #286450 |
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— | over 2 years ago |
| Edit | Post #286450 |
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— | over 2 years ago |
| Edit | Post #286450 | Initial revision | — | over 2 years ago |
| Answer | — |
A: $g(x)\xrightarrow{x\to\infty}\infty$ Implies $g'(x)\leq g^{1+\varepsilon}(x)$ My questions 1. Can you cite or scan the question from the source? I am leery, because the claim appears false. 2. Is g(x) supposed to be convex? Game plan I shall construct, on top of $f(x)=x$, a function which occasionally jumps up a constant amount over littler and littler intervals... (more) |
— | over 2 years ago |
| Comment | Post #286428 |
Want to add this too on https://old.reddit.com/r/math/ or https://old.reddit.com/r/mathematics ? You can just click "Submit a new link", then copy and paste the URL here. (more) |
— | over 2 years ago |
| Edit | Post #281985 |
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— | over 3 years ago |
| Edit | Post #281985 |
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— | over 3 years ago |
| Edit | Post #281985 |
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— | over 3 years ago |
| Edit | Post #281985 |
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— | over 3 years ago |
| Edit | Post #281985 |
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— | over 3 years ago |
| Edit | Post #281985 | Initial revision | — | over 3 years ago |
| Question | — |
Why can an easily graphable definite integral, be labyrinthine to evaluate? How can I explain to 16-year-olds, who just started calculus, why it's so nettlesome and tricky to symbolically integrate definite integrals, when their graph looks so unremarkable and straightforward? I used Desmo to graph $\int0^{\pi/2}\frac{x^2\log^2{(\sin{x})}}{\sin^2x} \, dx$ below. u/camel... (more) |
— | over 3 years ago |
| Edit | Post #281010 |
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— | over 3 years ago |
| Edit | Post #281010 | Initial revision | — | over 3 years ago |
| Question | — |
De-mystifying tricks – If $\{x_n\}$ converges, then Cesaro Mean converges. >Exercise 2.3.11 (Cesaro Means). (a) Show if $\{xn\}$ is a convergent sequence, then the sequences given by the averages $\{\dfrac{x1 + x2 + ... + xn}{n}\}$ converges to the same limit. I rewrote and colored the official solution. >Let $\epsilon>0$ be arbitrary. Then we need to find an $N \... (more) |
— | over 3 years ago |
| Edit | Post #281009 |
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— | over 3 years ago |
| Edit | Post #281009 | Initial revision | — | over 3 years ago |
| Question | — |
Why aren't $z_1=f(xy)$ and $z_2=f(x/y)$ functions of 2 variables? Hagen von Eitzen answered that $z1, z2$ >depend on only one variable - there's no comma between the parentheses. John Doe commented >the function $f(xy)=e^{xy}sin(xy)+(xy)^3$ may look like a multivariable function in x and y, but it can be written more simply as a univariate function, $f(t... (more) |
— | over 3 years ago |
| Edit | Post #280851 |
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— | over 3 years ago |
| Comment | Post #280864 |
Can you please respond in, by editing, your answer? Comment chains are
cumbersome to read.
(more) |
— | over 3 years ago |
| Comment | Post #280864 |
(3) "x has been fixed right at the beginning as an arbitrary positive real number." You spotted my issue! Can you please elaborate? Why can you just assume or deudce that x is fixed? As you wrote, "Stewart expects this to be clear from the phrasing of the exercise itself, and does not begin the solut... (more) |
— | over 3 years ago |
| Comment | Post #280864 |
Thanks. (1) "I confess I don't see the difference between the two statements." You're correct. There isn't. I edited my post to elaborate. (2) "my variables are " (I think you meant to say "x and m", or "variable is"?) Yes. Thanks. I corrected this. (more) |
— | over 3 years ago |
| Edit | Post #280851 |
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— | over 3 years ago |
| Comment | Post #280851 |
@r~~ Do you mean https://i.imgur.com/i5jxtFW.jpg? "you're using images of text instead of writing your question such that no images are required" Images ARE required. I don't want to mis type the solution manual. I want to show you exactly what it says.
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— | over 3 years ago |
| Edit | Post #280856 |
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— | over 3 years ago |
| Edit | Post #280856 |
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— | over 3 years ago |
| Edit | Post #280856 | Initial revision | — | over 3 years ago |
| Question | — |
Don't downvote just because someone posted screenshot. I've seen comments of admitting to downvoting a post just because that poster posted screenshots. If someone is writing math, then they ought use MathJax, not screenshots. But if you're quoting someone else, especially if you are alleging someone else made a typo or mistake, then screenshots a... (more) |
— | over 3 years ago |
| Comment | Post #280851 |
@PeterTaylor Yes. https://i.imgur.com/mA64hx0.jpg (more) |
— | over 3 years ago |
| Edit | Post #280851 |
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— | over 3 years ago |
| Edit | Post #280851 |
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— | over 3 years ago |
| Edit | Post #280851 | Initial revision | — | over 3 years ago |
| Question | — |
If $n = xm$ and $n \rightarrow \infty$, then $m \rightarrow \infty$? Did Stewart prove the titular result, also underlined in green in the image below, either by himself or as an exercise, in Calculus Early Transcendentals or in the normal version Calculus? I attempted the proof, but I got nonplussed. $\infty = \lim\limits{n \rightarrow \infty} n = \lim\limits{n \r... (more) |
— | over 3 years ago |
| Edit | Post #280663 |
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— | over 3 years ago |
| Comment | Post #280717 |
Thanks. Can you please edit my scan and draw or write in what you mean? (more) |
— | over 3 years ago |
| Edit | Post #280663 |
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— | almost 4 years ago |