The point $P(2,\ln{2})$ lies on the curve $y=\ln{x}$.
(a) If $Q$ is the point $(x,\ln{x})$, find the slope of the secant line $PQ$ correct to four decimal places for the following values of $x$:

(1) 1.5         (2) 1.9
(3) 1.99       (4) 1.999
(5) 2.5         (6) 2.1
(7) 2.01       (8) 2.001

(b) Guess the slope of the tangent line to the curve at $P$.
(c) Using the slope from part (b), find the equation of the tangent line to the curve at $P$.

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(b)
(c)