Question

Determine why the following statement is true or false. (posted as a comment)

Answer 1

Please explain it though, I dont want the answer. I need to understand this

Answer 2

\[\lim_{x\to 1^+}\sqrt{x-1}=0\] because \(x\) is approaching 1 through numbers larger than 1, so the square root is defined

Answer 3

but
\[\lim_{x\to 1^-}\sqrt{x-1}\] does not exist, because as \(x\) goes to one through numbers smaller then 1, \(x-1\) is negative, and so the square root is not defined

Answer 4

if you look at a graph of \(y=\sqrt{x-1}\) it does not exist for values of \(x\) that are less than 1, so you cannot take the limit from the left

Answer 5

Ohhh! okay, thank you sooo much! that really helped