Find lim f(x) x-->2

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Find lim f(x) x-->2

Mathematics
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Do you remember what the definition of a limit is?
\[f(x)\left\{ e^x, x \le2 \right\}\left\{ xe^2, x>2 \right\}\]
the value a graph approaches from both sides.

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Other answers:

You must evaluate left and right limit.
Compare both right and left. If they are both equal to L, then the actual limit is L. If they aren't both equal to L, then the limit doesn't exist.
so how do you figure out what e^x equals
as x approaches 2... well e^x exists and is continuous at x=2 just use direct substitution
The options are 1, e, e^2, 2e^2, and non existent
i'm not supposed to use a calculator
I didn't say use a calculator
so how do you solve e^2 without a calculator
I said to evaluate both left and right limits.. you don't .... it is just e^2 for the left limit \[\lim_{x \rightarrow 2^-}f(x)=\lim_{x \rightarrow 2^-}e^x =\lim_{x \rightarrow 2}e^x=e^2 \\ \text{ now also find } \lim_{x \rightarrow 2^+}f(x)=\lim_{x \rightarrow 2^+} x e^{2}=\lim_{x \rightarrow 2} xe^{2}=?\]
again just use direct substitution since the function xe^2 is defined and continuous at x=2
I could just say continuous since continuous includes that is defined so xe^2 is continuous at x=2 so you can just use direct sub
@Reid448 are you still there?:
sorry study hall ended and i had to drive home from school. so the answer is lim f(x) = undefined x-->2
the limit does not exist since left did not equal right that is we know e^2 is not the same as 2*e^2
ok that makes sense. thx for the help

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