limits e^x are different in +infinite and minus infinite. But calculator does not show DNE. Why? Theory says that limit in infinity is not ?
- Anonymous1 month ago
The question is not clear. But this may help…
When dealing with real numbers, a limit is a finite, real number. For example a limit can -30, 0, 22.3 or π.
A limit cannot be infinity (or -infinity).
For example, if you approach x=0 ‘from the left’ or ‘from the right’ you get the same value (eˣ = e⁰ = 1) from both directions. That’s because eˣ is a continuous function of x in the interval (-∞, -∞).
For x→-∞ we can only approach from one direction. But that does not matter.
As x→-∞, eˣ → 0. The limit of eˣ exists (it is zero).
Bur for x→∞, eˣ →∞. The limit of eˣ does not exist (because infinity is not allowed as a limit).
- rotchmLv 71 month ago
e^20 = +BIG
e^-20 = +~0
Do a few more. Graph e^x (type e^x in Google). See whats going on?
Also, e^x as x --> infinity gives infinity. But sometimes, some calculators, some books or authors, say that 'infinite' is DNE. It depends on the language they adopt.
Infinity is not a number, hence it being called DNE sometimes.
Hope this clarifies a few things.
- ?Lv 71 month ago
e^x approaches + infinity as x approaches + infinity. As x approaches - infinity, e^x approaches zero.
See the graph of e^x.
Note that e^x is > 0 for all real x.