Evaluate the limit ( sqrtx - 3 ) / ( x^2 - 9 ) x-->3

We have to calculate lim [(sqrt
x-3)/(x^2-9)].

We'll follow the
steps:

-we'll write the difference of squares
as:

x^2 - 9 =
(x-3)(x+3),

Also, we could consider x - 3 as a difference
of squares.

x-3 =
(sqrtx-sqrt3)(sqrtx+sqrt3)

We'll evaluate the
limit:

lim [(sqrt x-3)/(x^2-9)]=lim [(sqrt
x-3)/(sqrtx-sqrt3)(sqrtx+sqrt3)]

We'll substitute x by 3,
into the limit:

lim (sqrt3 -
3)/(sqrtx+sqrt3)(sqrt3-sqrt3)

lim [(sqrt
x-3)/(x^2-9)] = (sqrt3 -
3)/0*(sqrtx+sqrt3)

lim
[(sqrt x-3)/(x^2-9)] =
+infinite