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## #1 2017-12-30 11:44:30

Hannibal lecter
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Registered: 2016-02-11
Posts: 222
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### what is the solution for f(x) = exp(-x) ?

Hi, is there a root for the f(x) = e^-x ???

is it close to 0.571143115080177? or that wrong there is no any root?

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #2 2017-12-30 14:51:23

ganesh
Registered: 2005-06-28
Posts: 24,267

### Re: what is the solution for f(x) = exp(-x) ?

Hi,

Hope this graph helps:

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2017-12-31 05:10:30

zetafunc
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Registered: 2014-05-21
Posts: 2,188
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### Re: what is the solution for f(x) = exp(-x) ?

Hannibal lecter wrote:

Hi, is there a root for the f(x) = e^-x ???

is it close to 0.571143115080177? or that wrong there is no any root?

raised to the power of anything won't ever have a root, because the exponential function is always positive. You can see this in the graph that ganesh posted -- it won't ever touch (nor go below) the x-axis.

Where did you get 0.571143115080177 from? Are you stating the problem correctly? Or is something else meant by the word 'root' here?

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## #4 2018-01-04 09:05:55

Hannibal lecter
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Registered: 2016-02-11
Posts: 222
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### Re: what is the solution for f(x) = exp(-x) ?

I tried a matlab code to solve it, but thanks for helping I know it's nor have a root now..

Wisdom is a tree which grows in the heart and fruits on the tongue

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## #5 2018-01-04 23:00:18

Member
From: Planet Mars
Registered: 2016-11-15
Posts: 766

### Re: what is the solution for f(x) = exp(-x) ?

zetafunc wrote:

Where did you get 0.571143115080177 from?

See the graph which Ganesh posted. You will see that it converges down to X-axis and almost touches it at that value.

Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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## #6 2018-01-05 01:42:19

bob bundy
Registered: 2010-06-20
Posts: 8,322

### Re: what is the solution for f(x) = exp(-x) ?

See here:

http://www.mathsisfun.com/data/function … nc1=e^(-x)

Just add y = x as the second function and you'll see it does have that value as the solution.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #7 2018-01-06 01:24:06

zetafunc
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Registered: 2014-05-21
Posts: 2,188
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### Re: what is the solution for f(x) = exp(-x) ?

See the graph which Ganesh posted. You will see that it converges down to X-axis and almost touches it at that value.

No, it doesn't ever touch the x-axis. The exponential function is strictly positive: it can't have any roots.

However, if we take
, then there is indeed a root. In fact, if we allow complex solutions, there are infinitely many of them, and they are precisely the nth values of the Lambert-W function,
. This sequence generates all the complex roots.

There is one real root, the so-called Omega constant,
. There are several exact forms for the Omega constant, such as the 'power tower':

and a nice integral relation is:

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