in my textbook it says this:
lim x-->infinty square root (x^2+x) - x **note the x^2+x is under the root only
is the same as square root (x^2) - x **the x^2 is under the root only
which is lim x--> infinity (x-x) = 0
Question 1: Can someone please explain how we get 0 (especially the part where square root(x^2+x) becomes square root(x^2)
Question 2: under this example in the book it says "it can be shown that the limit in the above question is not 0 but is 1/2 --?? what the heck does that mean they just showed that it equals 0 now they're saying it equals 1/2 ??
can someone explain both please