lim [sqrt(1+x)-sqrt(x-1)]
x->infinity
i tried to move it to the denominator like this:
lim 1/[sqrt(x+1)+sqrt(x-1)]
but here im stuck, i think it should be zero, but hoe do i prove it?
thanks in advance.
Depends on "how much rigour" you want...
You could always go back to the definition, but I wouldn't do that unless necessary.
Multiply numerator and denominator with the complement of the numerator to get:
Now the numerator is constant and positive and the denominator clearly goes to +infinity, yielding 0 as limit.