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In calculus, when evaluating the limit of a function as the variable approaches a certain point, we sometimes encounter expressions that are undefined or difficult to evaluate directly. These are known as indeterminate forms. Common examples include forms like \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \).

When faced with an indeterminate form, standard algebraic manipulation or calculus techniques are typically employed to resolve the form. This is crucial as indeterminate doesn't mean the limit doesn't exist, but rather requires a deeper analysis.

In our specific calculus limit problem, substituting \( x = -3 \) into the function initially results in a \( \frac{0}{6} \) form, which is not indeterminate. Therefore, the limit can be evaluated directly without further manipulation. However, if it had resulted in \( \frac{0}{0} \), we would need to find alternative ways to simplify or rewrite the function.

A function is said to be continuous at a point if the limit of the function as \( x \) approaches that point is equal to the function's value at that point. This implies there is no jump or break in the graph of the function at that point.

Continuity ensures the smoothness of the function around the point being evaluated. For our problem, when \( x = -3 \) is substituted into the denominator and numerator of \( \frac{x^2 + 2x - 3}{x^2 + x - 6} \), the output is not an indeterminate form, suggesting that the function behaves well near \( x = -3 \) and is continuous at this point.

If continuity is established, it is usually straightforward to evaluate the limit, as the function doesn't exhibit any unexpected behavior around that point. This helps clarify analysis as limits approach the given point from both sides in a similar manner.

Evaluating limits is a fundamental idea in calculus, representing how a function behaves as it nears a specific point. It provides insight into function behavior near boundaries or points of interest without necessarily reaching them.

The process involves substituting the approaching value into the function and checking the form that arises. Often limits can be evaluated directly, but indeterminate forms, as discussed earlier, may require additional methods such as L'Hôpital's Rule or algebraic manipulation.

In this example, when evaluating the limit of \( \frac{x^2 + 2x - 3}{x^2 + x - 6} \) as \( x \to -3^- \), we substitute \( x = -3 \) and arrive at a clear value of 0, since the substitution does not lead to any undefined expression. This means the limit from the left-hand side is simply the evaluated function, conforming with the concept of function continuity.