If `f(x) = (x)/(1+(log x)(log x)....oo), AA x in [1, 3]` is non-differentiable at x = k. Then, the value of `[k^(2)]`, is (where `[*]` denotes greatest integer function).

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the problem, we need to analyze the function given by:

\[ f(x) = \frac{x}{1 + (\log x)(\log x) + (\log x)(\log x)(\log x) + \ldots} \]

This series continues indefinitely. We can express it in terms of limits.

### Step 1: Rewrite the function using limits
We can express the infinite series in terms of limits. The function can be rewritten as:

\[ f(x) = \lim_{n \to \infty} \frac{x}{1 + (\log x)^n} \]