### Problem 8

8. Find the best linear approximation for ln x which is tangent to
the graph of the function when x = 1. Use this to approximate ln
1.05. Check your answer with a calculator.

The formula for the best linear approximation to y = f(x) at a
point where x = a is

f(x) = f(a) + f'(a)(x - a)
If f(x) = ln x and a = 1, we get

ln(x) = ln 1 + x - 1
= 0 + x - 1
= x - 1
To use this to approximate ln 1.05,

1.05 - 1 = 0.05
According to a calculator

ln 1.05 = 0.048790164