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## Homework Statement

If the lim

_{x→b}f(x)=c, then lim

_{x→b}e

^{x}= e

^{c}. What property of the function g(x)=e

^{x}allows this fact?

## The Attempt at a Solution

Is it just because e is a constant?

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- Thread starter brunokabahizi
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- #1

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If the lim

Is it just because e is a constant?

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HallsofIvy

Science Advisor

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That property pretty much

The function f(x) is continuous at x= a if and only if

(1) f(a) exists.

(2) [itex]\lim_{x\to a} f(x)[/itex] exists.

(3) [itex]\lim_{x\to a} f(x)= f(a)[/itex].

Since (3) pretty much implies the left and right sides exist, of only that is given as the definition- but that's really "shorthand".

- #5

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That's why I said continuity is the key. The theorem seems to be easy to be proved though.

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