Question

Find the limit if it exists:

lim x->infinity

x[ln(x+4)-ln(x)]

Answer 1

ive gotten this far:
x/(1/x+4)-(1/x)

Answer 2

ok, well the term ln(x) as it approaches infinity is infinity

Answer 3

so for the part of the brackets you'll have a number that is positive and approaching infinity

Answer 4

so, that means the entire term is approaching positive infinity

Answer 5

thanks again yosh

Answer 6

np

Answer 7

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.