Question

what the limit as x goes to infinity of the function ----xln(1-(10/x))????

Answer 1

Take it by parts what is x as x goes to infinity?

Answer 2

0

Answer 3

or 1

Answer 4

try again infinity, next part on the inside what happens when 10 or any number is over infinity?

Answer 5

o ya i see x goes to infinity, um its infinity? thats what your asking ?

Answer 6

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?

Answer 7

x gets smaller?

Answer 8

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.

Answer 9

yes it maks sense ... i know what you were asking now ...

Answer 10

So you have the first x going to infinity and that is multiplied by ln (1-0). What is ln 0?

Answer 11

I'm sorry ln 1

Answer 12

0?

Answer 13

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?

Answer 14

lhospital rule?

Answer 15

Right on apply l'hopital to the original equation.

Answer 16

see im having trouble that part

Answer 17

i sec

Answer 18

yeah, product rule u'v+uv'

Answer 19

ya i get (x/(1-10/x))+ln(1-(10/x))....

Answer 20

Yeah, you might be off one piece ln (1-10/x) + (10x^3)/(1-10/x)

Answer 21

Ok, find lim, you found already that ln (1-10/x) goes to zero so just concentrate on last part

Answer 22

You also found that (1-10/x) goes to 1-0 which is 1. So just find lim 10x^3

Answer 23

how did you get 10x^3??

Answer 24

how did you get 10x^3??

Answer 25

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