Evaluate:`underset( x rarr 2) ( "lim") (x-2)/(root(3)(x)-root(3)(33))`

Explanation

Given limit: `lim_(x->2)\ (x-2)/(root(3)(x)-root(3)(33))`
Substituting 2 as we get an indeterminant form of `(0/0)`
As it has come as `(0/0)` form ,so we use L’Hospitals Rule.
now by using L’Hospitals Rule the limit is given by,
`l=lim_(x->2)(1/((1/3)(x^(-2/3))))`
`=2^(2/3)/(1/3)`
`=3*2^(2/3)`