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.