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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...
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over 1 year ago
Edit Post #287647 Post edited:
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...
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almost 2 years ago
Comment Post #287625 @#53398 I recast my post. Better now?
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almost 2 years ago
Edit Post #287625 Post edited:
almost 2 years ago
Edit Post #287625 Post edited:
almost 2 years ago
Edit Post #287625 Post edited:
almost 2 years ago
Edit Post #287625 Post edited:
almost 2 years ago
Edit Post #287625 Post edited:
almost 2 years ago
Edit Post #287625 Post edited:
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...
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almost 2 years ago
Edit Post #286450 Post edited:
over 2 years ago
Edit Post #286450 Post edited:
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...
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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.
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over 2 years ago
Edit Post #281985 Post edited:
over 3 years ago
Edit Post #281985 Post edited:
over 3 years ago
Edit Post #281985 Post edited:
over 3 years ago
Edit Post #281985 Post edited:
over 3 years ago
Edit Post #281985 Post edited:
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...
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over 3 years ago
Edit Post #281010 Post edited:
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 \...
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over 3 years ago
Edit Post #281009 Post edited:
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...
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over 3 years ago
Edit Post #280851 Post edited:
almost 4 years ago
Comment Post #280864 Can you please respond in, by editing, your answer? Comment chains are cumbersome to read.
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almost 4 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...
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almost 4 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.
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almost 4 years ago
Edit Post #280851 Post edited:
almost 4 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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almost 4 years ago
Edit Post #280856 Post edited:
almost 4 years ago
Edit Post #280856 Post edited:
almost 4 years ago
Edit Post #280856 Initial revision almost 4 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...
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almost 4 years ago
Comment Post #280851 @PeterTaylor Yes. https://i.imgur.com/mA64hx0.jpg
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almost 4 years ago
Edit Post #280851 Post edited:
almost 4 years ago
Edit Post #280851 Post edited:
almost 4 years ago
Edit Post #280851 Initial revision almost 4 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...
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almost 4 years ago
Edit Post #280663 Post edited:
almost 4 years ago
Comment Post #280717 Thanks. Can you please edit my scan and draw or write in what you mean?
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almost 4 years ago
Edit Post #280663 Post edited:
almost 4 years ago