Question

hw 2.2
score: 2.75/8 answered: 3/8
question 4
evaluate the limit: \\(\lim_{x \to 5} \frac{x^2 - 11x + 30}{x - 5}\\)
question help: video

Explanation:

Step1: Factor the numerator

We factor the quadratic expression \(x^2 - 11x + 30\). We need two numbers that multiply to \(30\) and add up to \(-11\). Those numbers are \(-5\) and \(-6\). So, \(x^2 - 11x + 30=(x - 5)(x - 6)\).
The limit becomes \(\lim_{x
ightarrow5}\frac{(x - 5)(x - 6)}{x - 5}\)

Step2: Cancel the common factor

Since \(x
ightarrow5\) but \(x
eq5\) (we are taking the limit, not evaluating at \(x = 5\)), we can cancel the common factor \((x - 5)\) from the numerator and the denominator.
After canceling, we get \(\lim_{x
ightarrow5}(x - 6)\)

Step3: Evaluate the limit

Now we substitute \(x = 5\) into the expression \(x - 6\).
\(5-6=-1\)

Answer:

\(-1\)