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Important limit

x^ke^-x

If i increase x from 22 -> 30
Using k = 60

x^ke^-x tends to infinity?
Original post by Zenarthra
x^ke^-x

If i increase x from 22 -> 30
Using k = 60

x^ke^-x tends to infinity?


well if x tends to 30 then xke−xx^ke^{-x} won't tend to infinity... It will tend to whatever 3060e−3030^{60}e^{-30} is

Either that or I don't understand your question?
(edited 9 years ago)
Original post by Zenarthra
x^ke^-x

If i increase x from 22 -> 30
Using k = 60

x^ke^-x tends to infinity?


Sorry your question is fairly confusing, is it:

xke−xx^{ke^{-x}}

and why are you looking at a particular range for x? Does the question specify?
Reply 3
Avatar for Zenarthra
Zenarthra
OP
3
Original post by TheIrrational
well if x tends to 30 then xke−xx^ke^{-x} won't tend to infinity... It will tend to whatever 3060e−3030^{60}e^{-30} is

Either that or I don't understand your question?


Original post by Slowbro93
Sorry your question is fairly confusing, is it:

xke−xx^{ke^{-x}}

and why are you looking at a particular range for x? Does the question specify?



It is what irrational has wrote.
If x -> infinity with k = 60 does the value of x^ke^-x not increase?
Original post by Zenarthra

If x -> infinity with k = 60 does the value of x^ke^-x not increase?


Up to a point, and then decreases.

xke−x=xkexx^ke^{-x}=\dfrac{x^k}{e^x} and you should know that the exponential function eventually increases faster than any polynomial.
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Avatar for davros
davros
16
Original post by Zenarthra
It is what irrational has wrote.
If x -> infinity with k = 60 does the value of x^ke^-x not increase?


If k is fixed and positive then the limit of xke−xx^ke^{-x} is 0 as x tends to infinity.
Reply 6
Avatar for Zenarthra
Zenarthra
OP
3
Original post by ghostwalker
Up to a point, and then decreases.

xke−x=xkexx^ke^{-x}=\dfrac{x^k}{e^x} and you should know that the exponential function eventually increases faster than any polynomial.


Original post by davros
If k is fixed and positive then the limit of xke−xx^ke^{-x} is 0 as x tends to infinity.



Ah right, i tried a few more values/
Thanks!

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