Estimate the slope of the tangent line (rate of change) to $\displaystyle {f{{\left({x}\right)}}}=\frac{{1}}{{x}}$ at $\displaystyle {x}={2}$ by finding the slopes of the secant lines through the points listed below. Then calculate the slope of the tangent line at the given point.

State answers to three decimal places

1. $\displaystyle {\left({1.8},\frac{{1}}{{1.8}}\right)}$ and $\displaystyle {\left({2.2},\frac{{1}}{{2.2}}\right)}$
   
   secant slope, $\displaystyle {m}_{{{\sec}}}=$
   
   
2. $\displaystyle {\left({1.9},\frac{{1}}{{1.9}}\right)}$ and $\displaystyle {\left({2.1},\frac{{1}}{{2.1}}\right)}$
   
   secant slope, $\displaystyle {m}_{{{\sec}}}=$  
3. slope of the tangent line,    $\displaystyle {m}_{{{t}}}=$