1 Answer

Jumhyn · Answer 1 · 2023-09-19T15:42:34+0000

Since
is approaching 1 from the left/below, we take the part of
f(x) that is defined over
x<1 , for which we have

f(x) = (x-1)/(√(x-1))

Since
$x\\eq1$ , we can simplify this to

f(x) = (x-1)/((x-1)^(1/2)) = (x-1)^(1/2) = √(x-1)

and this is continuous at
x=1 , so we can evaluate the limit by directly substituting
.

To summarize:

$\displaystyle \lim_(x\to1^-) f(x) = \lim_(x\to1) (x-1)/(√(x-1)) = \lim_(x\to1) √(x-1) = √(1-1) = \boxed{0}$

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