anonymous
  • anonymous
what the limit as x goes to infinity of the function ----xln(1-(10/x))????
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Take it by parts what is x as x goes to infinity?
anonymous
  • anonymous
0
anonymous
  • anonymous
or 1

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anonymous
  • anonymous
try again infinity, next part on the inside what happens when 10 or any number is over infinity?
anonymous
  • anonymous
o ya i see x goes to infinity, um its infinity? thats what your asking ?
anonymous
  • anonymous
Yeah x goes to infinity, that is the first which is then multiplied by len (1-10/x). What happens when 10 or any number is over x as x goes to infinity?
anonymous
  • anonymous
x gets smaller?
anonymous
  • anonymous
No, just like earlier x goes to infinity. But the point is it is 10/x. Anytime a number is over infinity it goes to zero. There is a lot of situations in this problem that occurs a lot so you should take notes. That's not the complete answer yet. Let me know if what I am saying makes any sense.
anonymous
  • anonymous
yes it maks sense ... i know what you were asking now ...
anonymous
  • anonymous
So you have the first x going to infinity and that is multiplied by ln (1-0). What is ln 0?
anonymous
  • anonymous
I'm sorry ln 1
anonymous
  • anonymous
0?
anonymous
  • anonymous
Right so, if you are keeping tracking you have the lim of infinity times zero. That is a special condition. Check your classroom notes: what to do?
anonymous
  • anonymous
lhospital rule?
anonymous
  • anonymous
Right on apply l'hopital to the original equation.
anonymous
  • anonymous
see im having trouble that part
anonymous
  • anonymous
i sec
anonymous
  • anonymous
yeah, product rule u'v+uv'
anonymous
  • anonymous
ya i get (x/(1-10/x))+ln(1-(10/x))....
anonymous
  • anonymous
Yeah, you might be off one piece ln (1-10/x) + (10x^3)/(1-10/x)
anonymous
  • anonymous
Ok, find lim, you found already that ln (1-10/x) goes to zero so just concentrate on last part
anonymous
  • anonymous
You also found that (1-10/x) goes to 1-0 which is 1. So just find lim 10x^3
anonymous
  • anonymous
how did you get 10x^3??
anonymous
  • anonymous
how did you get 10x^3??
anonymous
  • anonymous
Product rule u is x, u' is 1; v is ln (1-10/x), v' (10x^2)/(1-10/x) Put it together u'v +uv' is ln (1-10/x) + (x10x^2)/(1-10/x) -->ignore everything as stated earlier and the last part is x10^2 --> 10^3

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