Question

How do you evaluate the limit `x-sqrt(x^2+x)` as x approaches `oo`?

Answer 1

`= - 1/2`

Explanation:

`lim_(x to oo) x-sqrt(x^2+x)`

`= lim_(x to oo) x-x (1+1/x)^(1/2)`

and Binomial expansion

`= lim_(x to oo) x-x (1+1/2 *1/x + O (1/x^2) )`

`= lim_(x to oo) x- x - 1/2 + O(1/x)`

`= - 1/2`