Question

\lim_{x \rightarrow 0} e ^{(1/x*\log x)}

Answer 1

\[ \lim_{x \rightarrow 0+} 1/x = +\infty \ \ and \ \ \lim_{x \rightarrow 0+} ln x = -\infty\]

Hence
\[ \lim_{x \rightarrow 0+} (ln x)/x = -\infty \]
Thus ... what does this tell you about your limit?

Answer 2

not defined??

Answer 3

Oh, come on.

What is
\[\lim_{x \rightarrow -\infty} \ e^x\]
?

Answer 4

my question is \[\lim_{x \rightarrow 0}e ^{(1/x*\log x)}\]

Answer 5

i meant e raised to

Answer 6

Yes, I just showed you how the index goes to -infinity. Now what happens to the function e^x as x --> -infinity?

Answer 7

not defined is the answer?

Answer 8

No.

Let me brak this down ever further for you.

Let y(x) = (ln x)/x

Then limit y(x) as x --> 0+ is -infinity, agreed?

Answer 9

Now what is
\[\lim_{y \rightarrow -\infty} e^y\]

Answer 10

yes

Answer 11

-infinity

Answer 12

No ... that's a bad error. What does the graph of the exponential function look like?

Answer 13

pls tel final answer i hav many othr questions to do :(

Answer 14

The limit of e^y as y --> -infinity is zero.

Answer 15

hence your limit is what ... ?

Answer 16

+infinity

Answer 17

What is
\[\lim_{y \rightarrow -\infty} \ e^y\]
?

Answer 18

sorry to butt in, but please James, just have a look at my question when you get the chance, it should be easy for you.

Answer 19

tl the FINAL ANSWER PLZZZZZZZZZZZZZZZZZZZZZZZ

Answer 20

@TT: ok

Answer 21

If you don't understand this basic property of the exponential that the limit as y-->-infinity is zero, you'll be in deep trouble later.

The answer is this:
\[y(x) = (\ln x) / x\]
\[\lim_{x \rightarrow 0+} y(x) = -\infty \]
\[ \lim_{y \rightarrow -\infty} e^y = 0\]
therefore
\[\lim_{x \rightarrow 0+} e^{(ln x)/x} = 0\]