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Evaluate the following limit: underset( ...

Evaluate the following limit: `underset( x rarr 0) ( "lim")(2x)/(sqrt(a+x)-sqrt(a-x))`

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`(lim)_(x->0)(2x)/(sqrt(a+x)-sqrt(a-x))`

Multiplying with conjugate:

`(lim)_(x->0)((2x)(sqrt(a+x)+sqrt(a-x)))/(a+x-a+x)`

`(lim)_(x->0)((2x)(sqrt(a+x)+sqrt(a-x)))/(2x)`

`(lim)_(x->0) sqrt(a+x)+sqrt(a-x)`

`=sqrt(a+0)+sqrt(a-0)=2sqrt(a)`

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