Post History
#2: Post edited
by
TextKit
·
2021-02-02T21:25:53Z (over 3 years ago)
- I'm not asking about [the proof](https://math.stackexchange.com/a/3983012/872474) 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]][1]
- I can ask this as a separate question, but I feel that the underlying difficulty is the same. How can I visualize how Formula 8 shifts to Formula 9 below?
- [![enter image description here][2]][2]
- [1]: https://i.stack.imgur.com/6qyPn.jpg
- [2]: https://i.stack.imgur.com/0cwVM.jpg
- I'm not asking about [the proof](https://math.stackexchange.com/a/3983012/872474) 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]][1]
- I can ask this as a separate question, but I feel that the underlying difficulty is the same. How can I visualize how Formula 8 shifts to Formula 9 below?
- [![enter image description here][2]][2]
- James Stewart, *Calculus* 7th ed 2011. Not Early Transcendentals. p. 443 for the first image.
- [1]: https://i.stack.imgur.com/6qyPn.jpg
- [2]: https://i.stack.imgur.com/0cwVM.jpg
#1: Initial revision
by
TextKit
·
2021-02-02T21:22:23Z (over 3 years ago)
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](https://math.stackexchange.com/a/3983012/872474) 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]][1] I can ask this as a separate question, but I feel that the underlying difficulty is the same. How can I visualize how Formula 8 shifts to Formula 9 below? [![enter image description here][2]][2] [1]: https://i.stack.imgur.com/6qyPn.jpg [2]: https://i.stack.imgur.com/0cwVM.jpg