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Evaluate the following limit: underset( ...

Evaluate the following limit: `underset( x rarr 3) ( "lim")(x-3)/(sqrt(x-2)-sqrt(4-x))`

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`(lim)_(x->3)(x-3)/(sqrt(x-2)-sqrt(4-x))`

Multiplying with conjugate:

`(lim)_(x->3)((x-3)(sqrt(x-2)+sqrt(4-x)))/(x-2-4+x)`

`(lim)_(x->3)((x-3)(sqrt(x-2)+sqrt(4-x)))/(2(x-3))`

`(lim)_(x->3)((sqrt(x-2)+sqrt(4-x)))/(2)`

`=(sqrt(3-2)+sqrt(4-3))/(2)`

`=2/(2)=1`

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