# 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 ?

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• Anonymous
1 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).

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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).

• rotchm
Lv 7
1 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 7
1 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.