Interview Question for Private Wealth Management at Goldman Sachs:

the answer is 1/2, but it's incredibly difficult to do in your head. To talk your way through this, you should just start by plugging in numbers for x, hopefully you are good at doing square roots in your head, or have a calculator at the interview. Anyway, you could use x=2 which yields sqrt(6)-2 which equals 2.45-2= 0.45, then use x=3 which yields sqrt(12)-3 which equals 3.46-3=.46. Thus the limit approaches 1/2. Although wrong, another answer that you could use that demonstrates critical thinking ability and is pretty close to the real answer is 0, because as x gets larger, the addition of x to x^2 will become less and less significant, thus x^2 + x will get closer to x^2, and sqrt(x^2+x) will get closer to x. Thus you will get closer and closer to (x)-x, which is 0.