Answer:
The taylor's series for f(x) = ln x centered at c = 1 is:
[tex]ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }[/tex]
Step-by-step explanation:
The calculations are handwritten for clarity and easiness of expression.
However, the following steps were taken in arriving at the result:
1) Write the general formula for Taylor series expansion
2) Since the function is centered at c = 1, find f(1)
3) Get up to four derivatives of f(x) (i.e. f'(x), f''(x), f'''(x), [tex]f^{iv}(x)[/tex])
4) Find the values of these derivatives at x =1
5) Substitute all these values into the general Taylor series formula
6) The resulting equation is the Taylor series
[tex]ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }[/tex]
