Evaluate the following limit: `underset( x rarr a) ( "lim")(x-a)/(sqrt(x)-sqrt(a))`

Explanation

Given that limit: `lim_(x->a)(x-a)/(sqrt(x)-sqrt(a))`
`l=(a-a)/(sqrt(a)-sqrt(a))`
`=(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->a)(1-0)/((1/(2sqrt(x)))-0)`
`l=lim_(x->a)2(sqrt(x))`
`=2(sqrt(a))`