Activity for TextKit
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #280653 |
@DerekElkins "your question asks me to strain my eyes staring at blazing white boxes to figure out what you're asking." Apology! But I can't render pictures into text or MathJax??? (more) |
— | about 3 years ago |
| Comment | Post #280653 |
@DerekElkins "doesn't simply plotting $x = 1/t$ as a function of $t$ not already make it graphically and intuitively obvious that $t$ approaching $0^\pm$ causes $x$ to approach $\pm\infty$" Perhaps...but how can I visualize this change of variable right in this image, without plotting another graph? ... (more) |
— | about 3 years ago |
| Comment | Post #280653 |
@DerekElkins The first image pictures the LHS, i.e. $\lim\limits_{x \rightarrow \pm \infty} f(x)$. How can I visualize the RHS, or why the LHS = RHS, from this picture alone? (more) |
— | about 3 years ago |
| Edit | Post #280663 | Initial revision | — | about 3 years ago |
| Question | — |
How can I generalize a picture for the Mean Value Theorem to the Generalized MVT? How can I transmogrify this figure for the Generalized MVT? If $f$ and $g$ are continuous on the closed interval $[a, b]$ and differentiable on the open interval $(a, b)$, then $\exists$ $c ∈ (a, b) \ni \cfrac{f'(c)}{g'(c)} = \cfrac{f(b)-f(a)}{g(b)-g(a)}$. Please answer with a picture. Please... (more) |
— | about 3 years ago |
| Comment | Post #280639 |
Thanks. You're correct that the equality in question isn't in the text. But to clarify, are you implying that I was wrong to equate (32) with (33)? I explained how I did so in the last para. in my question, above the scan. (more) |
— | about 3 years ago |
| Edit | Post #280653 |
Post edited: |
— | about 3 years ago |
| Edit | Post #280653 | Initial revision | — | about 3 years ago |
| Question | — |
How can I visualize $\lim\limits_{x \rightarrow \pm \infty} f(x) = \lim\limits_{t \rightarrow 0^{\pm}} f(1/t)$? I'm not asking about the proof that I already understand. I'm longing to understand this graphically. As you can see, I added $1/t$ to Stewart's graphs. Then what? ![enter image description here][1] I can ask this as a separate question, but I feel that the underlying difficulty is the same. ... (more) |
— | about 3 years ago |
| Edit | Post #280630 | Initial revision | — | about 3 years ago |
| Question | — |
Why doesn't `\;` work? Kindly see https://math.codidact.com/posts/280629. `\;` isn't rendering? And I don't know why some of the MathJax is miffed? (more) |
— | about 3 years ago |
| Comment | Post #278382 |
@DerekElkins You're absolutely correct. (more) |
— | about 3 years ago |
| Edit | Post #280629 |
Post edited: |
— | about 3 years ago |
| Edit | Post #280629 | Initial revision | — | about 3 years ago |
| Question | — |
Isn't it wrong to write that Indefinite Integral = Definite Integral with a variable in its Upper Limit? >$\int f(t) \\; dt = \int{t0}^t f(s) \\; ds \quad \text{ where $t0$ is some convenient lower limit of integration.}$ Isn't this wrong? Because LHS $\neq$ RHS in general! Rather, LHS $\ni$ RHS, because LHS = RHS only if $C = -g(t0)$. By the Fundamental Theorem of Calculus (FTC), LHS = $\int... (more) |
— | about 3 years ago |
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