Question

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Answer 1

\[ \lim_{x\rightarrow 3} \frac{(x-3)(x+3)}{(x-3)} \]
the limit means let x approach 3, but *never actually equal 3*
In your expression (x-3) becomes very close to 0, but it never *is* zero.
In other words, we are allowed to divide by x-3 (because it is not zero)
and we have
\[
\lim_{x\rightarrow 3} x+3 \]
as x gets very close to 3, the sum x+3 gets very close to 3+3 i.e. 6
and we say the limit is 6:
\[ \lim_{x\rightarrow 3} x+3 =6\]

Answer 2

thank you!