How do I do this? Limits at infiinity?

Question

anonymous · Answer

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

amistre64 · Answer

simplify the right side using log rules

amistre64 · Answer

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.

amistre64 · Answer

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

jhannybean · Answer

Can you also use conjugates?

amistre64 · Answer

im not sure if thats useful here.  conjugates tend to be a form of multiplying by 1

(a-b)/(a-b)

amistre64 · Answer

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 ....