The point $P(1,1/2)$ lies on the curve $y=x/(1+x)$.

(a) If $Q$ is the point $(x,x/(1+x))$, find the slope of the secant line $PQ$ correct to four decimal places for the following values of $x$:

(1) .5           (2) .9
(3) .99         (4) .999
(5) 1.5         (6) 1.1
(7) 1.01       (8) 1.001

(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

(b) Guess the slope of the tangent line to the curve at $P$.

Slope =

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

$y=$