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

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=