A function `f(x)` is defined as `f(x)={(x^2 -x-6)/(x-3);ifx!=3 and 5ifx=3` Show that `f(x)` is continuous at `x=3.`

Explanation

To show that the function \( f(x) \) is continuous at \( x = 3 \), we need to verify that:

1. \( f(3) \) is defined.
2. The limit of \( f(x) \) as \( x \) approaches 3 exists.
3. The limit of \( f(x) \) as \( x \) approaches 3 is equal to \( f(3) \).

Let's go through these steps one by one.

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