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.
I have already found the slope of the secant line for each of the values, and guessed the slope of the tangent line to be 0.5. I am stuck on how to write the equation, I am sure I am overthinking it but is't the slope going to be 0.5? How do I find the y-intercept?