Question

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 \(\lim_{x
ightarrow6}\frac{(x + 6)(x - 6)}{x - 6}\).

Step2: Simplify the function

Cancel out the common factor \((x - 6)\) in the numerator and denominator (for \(x
eq6\)). The function simplifies to \(\lim_{x
ightarrow6}(x + 6)\).

Step3: Evaluate the limit

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

Answer:

12