# An indeterminate limit question

• March 22nd 2013, 09:33 AM
LLLLLL
An indeterminate limit question
Suppose lim x→1 (sqrt(ax+b)-2)/(x-1)=1, then a-b = ?

The answer key solved this by seeing the limit as 0/0, and therefore, sqrt(ax+b)-2 as 0.
What's the assumption, sqrt(ax+b)-2=0, based on?

If you substitute the value $x=1$ in the limit then the denominator is equal to $0$. This means the numerator can't be equal to some $L \in \mathbb{R}\setminus \{0\}$ as the limitvalue would be infinite then (i.e it would not exist). Hence the only possibility is that the numerator is equal to $0$ as $\frac{0}{0}$ is undefined.