lim x --> 0 for the function sqrt((1/x^2)-(1/x)) - sqrt((1/x^2)-(1/x))
Analyze the cases x > 0 and x < 0
The Attempt at a Solution
The solutions book simplifies the expression to
I know how to evaluate the limit from here. But I'm wondering why did they only place the absolute value sign for the single x in the denominator that multiplies with this (sqrt(1+x)+sqrt(1-x)) expression. Why isn't the absolute value sign around every single x?
The answer is that the limit doesnt exist.