Question

Evaluate.

Lim x->a (root x - roota)/tan(x-a)

Answer 1

L'Hopital's rule not allowed?

Answer 2

rationalize the numerator.
and also use tan=sin/cos

Answer 3

once you rationalize it, you will get a part with
sin (x-a)/(x-a) which equals 1 as sin x/x = 1 when x->0
in the other part you can directly put x=a