Question 834577
First ,let's do some manipulating,
{{{(sqrt(x+3) - sqrt(3)) /x= ((sqrt(x+3) - sqrt(3)) /x)*((sqrt(x+3)+sqrt(3))/(sqrt(x+3)+sqrt(3)))}}}
{{{(sqrt(x+3) - sqrt(3)) /x= (x+3-sqrt(3)sqrt(x+3)+sqrt(3)sqrt(x+3)-3)/(x*(sqrt(x+3)+sqrt(3)))}}}
{{{(sqrt(x+3) - sqrt(3)) /x= (x)/(x*(sqrt(x+3)+sqrt(3)))}}}
{{{(sqrt(x+3) - sqrt(3)) /x= 1/((sqrt(x+3)+sqrt(3))) }}}
Now we can take the limit,
{{{lim(x->0,((sqrt(x+3) - sqrt(3))) /x)=lim(x->0,(1/((sqrt(x+3)+sqrt(3)))))}}}
{{{lim(x->0,((sqrt(x+3) - sqrt(3))) /x)=1/((sqrt(3)+sqrt(3))))}}}
{{{highlight(lim(x->0,((sqrt(x+3) - sqrt(3))) /x)=1/(2*(sqrt(3))))}}}