What is the limit of #limxto1(sqrt(x+3)-2)/(x-1)#?

1 Answer
Mar 28, 2018

I got: #1/4#.

Explanation:

Have a look:
enter image source here

we could also try this:
Let us multiply top and bottom by #sqrt(x+3)+2#, we get:
#lim_(x->1)((sqrt(x+3)-2)/(x-1))(sqrt(x+3)+2)/(sqrt(x+3)+2)#
we would get:
#lim_(x->1)((x+3)-4)/((x-1)(sqrt(x+3)+2))#
#lim_(x->1)cancel((x-1))/(cancel((x-1))(sqrt(x+3)+2))#
as #x->1# we get:
#lim_(x->1)1/((sqrt(x+3)+2))=1/4#