« first day (614 days earlier)      last day (2203 days later) » 

Leaky Nun
Leaky Nun
12:45 AM
0
Q: Trouble calculating the limit $\lim_{x\to\infty} \frac{e^{-x}}{x^{-1}}$

Adam.VI want to find the limit $$\lim_{x\to\infty} \frac{e^{-x}}{x^{-1}}$$ Both sides go to 0, so I want to use L’Hospital’s Rule. However, when I differentiate both sides, I get $$\lim_{x\to\infty} \frac{-e^{-x}}{-x^{-2}}$$ Further differentiation doesn't yield anything useful either. How could I go...

differential-equations derivatives limits-without-lhopital
 
David Reed
David Reed
1:01 AM
@LeakyNun hey man its been awhile.
 
Leaky Nun
Leaky Nun
welcome back
 
David Reed
David Reed
thanks.
@LeakyNun Quick Question. The integral of a vector field will be path-independent if that field is a gradient ("fundamental theorem for line integrals"). Do you remember if the converse is also true?
 
Leaky Nun
Leaky Nun
no idea
 
David Reed
David Reed
no worries
I'm running into it in statistical thermodynamics--in which the concept is foundational
@LeakyNun Turns out the answer is yes, its an "iff"
 
Leaky Nun
Leaky Nun
nice
 
David Reed
David Reed
1:25 AM
What are you studying these days?
 

« first day (614 days earlier)      last day (2203 days later) »