Use linearization to approximate ln(9/10)

Answer 1

Start with the point (1,0), which lies on f(x) = lnx.

Then, f^'(x) = 1/x so f^'(1) = 1. The equation of the tangent line to f(x) at (1,0) is then y = x - 1 and at x=.9, y = -.1, which is the linear approximation of ln(.9).