Question

How do I do this? Limits at infiinity?

Answer 1

\[\lim_{x \rightarrow \infty}\ln(1+x)-\ln(x)\]

Answer 2

simplify the right side using log rules

Answer 3

then , divide every term by the highest power of x that exists in the setup; anything that has an x left under it goes to zero, the limit is whats left over.

Answer 4

i spose we could technically just split the fraction and it tuns into 1 + 1/x but thats just to simple to say lol

Answer 5

Can you also use conjugates?

Answer 6

im not sure if thats useful here. conjugates tend to be a form of multiplying by 1

(a-b)/(a-b)

Answer 7

ln(a) - ln(b) = ln(a/b)

after that, theres a few ways to consider it. same degree polys, splitting the fraction, dividing terms by highest power x, etc ....