Complete each table. Then estimate the given limit$.$

$6.\underset{x3}{lim}\sqrt[\phantom{2}]{2x-6}$

$\backslash$table$[[x,2\mathrm{.}9,2\mathrm{.}99,2\mathrm{.}999,3\mathrm{.}001,3\mathrm{.}01,3\mathrm{.}1],[f(x),,,,,,]]$

$\underset{x-3}{lim}\frac{x-3}{x^2-6x+9}$

$\backslash$table$[[x,-6x+9,,,,,],[x,2\mathrm{.}9,2\mathrm{.}99,2\mathrm{.}999,3\mathrm{.}001,3\mathrm{.}01,3\mathrm{.}1],[f(x),,,,,,]]$

$\underset{x0}{lim}\frac{\sqrt[\phantom{2}]{5}-\sqrt[\phantom{2}]{3}}{x}$

$\backslash$table$[[x=0,x,-0\mathrm{.}1,-0\mathrm{.}01,-0\mathrm{.}001,0\mathrm{.}001,0\mathrm{.}01],[f(x),,,,,,],[f(x),,,,,,]]$

$\underset{x-1}{lim}\frac{\frac{1}{x+3}-\frac{1}{2}}{x+1}$

$\backslash$table$[[x,-1\mathrm{.}1,-1\mathrm{.}01,-1\mathrm{.}001,-0\mathrm{.}999,-0\mathrm{.}99,-0\mathrm{.}9],[f(x),,,,,,]]$

$\underset{x0}{lim}\frac{sinx-1}{x}$

$\backslash$table$[[x,-0\mathrm{.}1,-0\mathrm{.}01,-0\mathrm{.}001,0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1],[f(x),,,,,,]]$