lim(x→6) (x² - 36)/(x - 6) what is the limit?

Explanation:

Step1: Factor the numerator

We know that (x^{2}-36=(x + 6)(x - 6)) by the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)) where (a=x) and (b = 6). So the limit becomes (\lim_{x\rightarrow6}\frac{(x + 6)(x - 6)}{x - 6}).

Step2: Simplify the function

Cancel out the common factor ((x - 6)) in the numerator and denominator (for (x\neq6)). The function simplifies to (\lim_{x\rightarrow6}(x + 6)).

Step3: Evaluate the limit

Substitute (x = 6) into (x+6). We get (6+6=12).

Answer:

12