1. ## Limits at Infinity

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 ??

2. Originally Posted by alisheraz19
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 ??

I think in the first instance they were probably talking about a mistake that students would probably make. while 1/2 is the actual answer. to get that 1/2 is the answer, the first step would be to multiply by $\frac {\sqrt{x^2 + x} + x}{\sqrt{x^2 + x} + x}$