evaluate the limit

Question

lim(x-√(x^2+1))

as x goes to infinity 

Answer 1

lim _x->∞(x-√(x²+1)) = lim _x->∞[(x-√(x²+1)) * (x+√(x²+1))/(x+√(x²+1))]

 

                               = lim _x->∞ [-1/(x+√(x²+1))]

 

                              = 0

Answer 2

Rationalize the numerator!

 

You now must evaluate lim (x→infinity) of -1/(2x), replacing x + sqrt(x²+1) by x + x)

and so you get zero.