The function `f(x)= xcos(1/x^2)` for `x != 0, f(0) =1` then at `x = 0, f(x)` is

Options

A. Continuous
B. Discontinuous
C. Not determined
D. None

Explanation

To determine the behavior of the function \( f(x) = x \cos\left(\frac{1}{x^2}\right) \) for \( x \neq 0 \) and \( f(0) = 1 \) at \( x = 0 \), we need to analyze the limit of \( f(x) \) as \( x \) approaches 0.

### Step-by-Step Solution:

1. **Identify the function and the point of interest**:
We have:
\[
f(x) =
...