Question

How do you find the limit `(2-sqrt(x+2))/(4-x^2)` as `x->2`?

Answer 1

I got: `1/16`

Explanation:

If you try to use `2` directly you get the indeterminate form `0/0`; we can try using De L'Hospital Rule deriving top and bottom and then apply the limit:
`lim_(x->2)((2-sqrt(x+2))/(4-x^2))=lim_(x->2)((-1/(2sqrt(x+2)))/(-2x))=`
as `x->2` we get:
`lim_(x->2)((-1/(2sqrt(x+2)))/(-2x))=1/16`