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

1 Answer
Gió
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

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