Evaluate the following limit: `lim_(x->1)(1-x^2)/(sinpix)`

Explanation

To evaluate the limit \( \lim_{x \to 1} \frac{1 - x^2}{\sin(\pi x)} \), we can follow these steps:

### Step 1: Substitute \( x = 1 \)
First, we substitute \( x = 1 \) into the expression to check the form of the limit:
\[ \frac{1 - (1)^2}{\sin(\pi \cdot 1)} = \frac{1 - 1}{\sin(\pi)} = \frac{0}{0} \]
Since we get the indeterminate form \( \frac{0}{0} \), we can apply L'Hôpital's Rule.
...