QuestionEvaluate $f(x)=\frac{x^{2}-3 x}{x^{2}-x-6}$ at $x=3.5,3.1,...,2.999$ and find $\lim_{x \to 3} f(x) \approx 0.600000$.

Studdy Solution
There seems to be a contradiction. The limit of the simplified function is3, but our guess based on the given values of $f(x)$ was0.6. This is because the original function is undefined at $x=3$. The function has a hole at $x=3$, and the value of the function at that point is defined to be the limit of the function as $x$ approaches3, which is0.6.
So, the correct answer is$$\lim_{x \rightarrow3} \frac{x^{2}-3 x}{x^{2}-x-6} =0.6$$