anonymous
  • anonymous
Find the limit if it exists: lim x->infinity x[ln(x+4)-ln(x)]
Mathematics
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anonymous
  • anonymous
Find the limit if it exists: lim x->infinity x[ln(x+4)-ln(x)]
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
ive gotten this far: x/(1/x+4)-(1/x)
anonymous
  • anonymous
ok, well the term ln(x) as it approaches infinity is infinity
anonymous
  • anonymous
so for the part of the brackets you'll have a number that is positive and approaching infinity

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anonymous
  • anonymous
so, that means the entire term is approaching positive infinity
anonymous
  • anonymous
thanks again yosh
anonymous
  • anonymous
np
anonymous
  • anonymous
Yeah you don't really need to do any work here. You know that ln(x+4) will be greater than ln(x) for all x. Therefore even if the difference between them was something very small, constant, and positive, the x out in front would grow without bound. So the whole expression would approach infinity. Now they're not going to stay constantly the same difference appart, but ln(x+4) will still be bigger than ln(x) you have something that goes to infinity times something else that goes to infinity. The result will go to infinity.

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