Instead of approximating ln x near x = 1, we approximate ln (1 + x) near x = 0. We get a simpler formula this way.

a. Derive the linearization ln (1 + x) ≈ x at x = 0.

b. Estimate to five decimal places the error involved in replacing ln (1 + x) by x on the interval 30, 0.14 .

c. Graph ln (1 + x) and x together for 0 ≤ x ≤ 0.5. Use different colors, if available. At what points does the approximation of ln (1 + x) seem best? Least good? By reading coordinates from the graphs, find as good an upper bound for the error as your grapher will allow.