Starting Limits HW Supposedly Easy

  • Thread starter Phyzwizz
  • Start date
  • #1
60
0
Just started learning limits today but I got stuck on this last problem...

Let f be the function given by f(x)=lnx/x for all x>0

Find lim f(x) as x-->0+

So I graphed the equation and plugged in points approaching zero on the right side but it seems to go on for infinity. Is the limit infinity? is that possible?
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
Yes. In fact it goes to -∞.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Uh, no, the limit is neither [itex]\infty[/itex] nor [itex]-\infty[/itex]. The limit, as x goes to 0, of ln(x) is [itex]-\infty[/itex] (which may be what LCKurtz meant) but that x in the denominator makes the limit 0. x goes to [itex]\infty[/itex] "faster" than ln(x) goes to [itex]-\infty[/itex].
 
  • #4
60
0
Awesome, thanks for the help guys. That clears things up. Oh and this doesn't have anything to do with limits, but how do you do the custom equations thing that makes the math equations on this site look so clean and wonderful.
 
  • #5
gb7nash
Homework Helper
805
1
Uh, no, the limit is neither [itex]\infty[/itex] nor [itex]-\infty[/itex]. The limit, as x goes to 0, of ln(x) is [itex]-\infty[/itex] (which may be what LCKurtz meant) but that x in the denominator makes the limit 0. x goes to [itex]\infty[/itex] "faster" than ln(x) goes to [itex]-\infty[/itex].

I don't follow this. If we're talking about:

[tex]\frac{ln(x)}{x}[/tex]

As x -> 0+, the numerator approaches -inf and the denominator approaches +0, so you should obtain -inf?
 
Last edited:
  • #6
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
Uh, no, the limit is neither [itex]\infty[/itex] nor [itex]-\infty[/itex]. The limit, as x goes to 0, of ln(x) is [itex]-\infty[/itex] (which may be what LCKurtz meant) but that x in the denominator makes the limit 0. x goes to [itex]\infty[/itex] "faster" than ln(x) goes to [itex]-\infty[/itex].

The limit is -∞. x → 0 in the denominator giving a -∞/0+ form.
 

Related Threads on Starting Limits HW Supposedly Easy

  • Last Post
Replies
2
Views
1K
Replies
4
Views
906
Replies
7
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
2K
Replies
5
Views
1K
Replies
3
Views
4K
  • Last Post
Replies
4
Views
5K
Top