Help me find this limit!

  • Thread starter swampwiz
  • Start date
  • #1
379
17
I can't seem to figure out how to find this seemingly simple limit (that is shown numerically to go to 0)

lim x → ∞ ( x rx )

for r < 1

This is an indeterminate form of ∞ * 0, but when I try to apply L'Hôpital's rule as

lim x → ∞ ( rx / ( 1 / x ) )

I end up getting an expression of the form x2 rx, with further application of the rule generating higher and higher powers of x

I'm totally stuck!
 

Answers and Replies

  • #2
gb7nash
Homework Helper
805
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You have the right idea. Try this instead:

lim x → ∞ (x/(1/r)x)
 
  • #3
379
17
You have the right idea. Try this instead:

lim x → ∞ (x/(1/r)x)
But wouldn't that be ∞ / ∞ ? L'Hopital's rule only applies to 0 / 0
 
  • #4
gb7nash
Homework Helper
805
1
L'Hopital's rule only applies to 0 / 0
No it doesn't. It also applies to +- inf/inf
 
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