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

(a) IfQ 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 :

(a) If

(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

Slope =

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

You can earn partial credit on this problem.