1. The problem asks us to understand the meaning of the limit statement: $$\lim_{x \to 2} f(x) = 6$$ and whether it is still true if $$f(2) = 7$$. 2. The limit $$\lim_{x \to a} f(x) = L$$ means that as $$x$$ gets arbitrarily close to $$a$$ (but not necessarily equal to $$a$$), the values of $$f(x)$$ get arbitrarily close to $$L$$. 3. Importantly, the value of $$f(a)$$ itself does not affect the limit. The limit depends only on the behavior of $$f(x)$$ near $$a$$, not at $$a$$. 4. So, even if $$f(2) = 7$$, the limit $$\lim_{x \to 2} f(x) = 6$$ can still be true as long as $$f(x)$$ approaches 6 when $$x$$ approaches 2 from either side. 5. In summary, the limit describes the trend of $$f(x)$$ near $$x=2$$, not the actual value at $$x=2$$. Final answer: Yes, the limit $$\lim_{x \to 2} f(x) = 6$$ can be true even if $$f(2) = 7$$.