Question

hw5 the limit laws (target l4; §2.3)
score: 8/13 answered: 8/13
question 9
evaluate the limit: $lim_{x \to 6}\frac{x^{2}-x - 30}{8x - 48}$

Explanation:

Step1: Factor the numerator and denominator

First, factor $x^{2}-x - 30=(x - 6)(x+5)$ and $8x - 48 = 8(x - 6)$.
So the limit becomes $\lim_{x
ightarrow6}\frac{(x - 6)(x + 5)}{8(x - 6)}$.

Step2: Cancel out the common factor

Since $x
eq6$ when taking the limit, we can cancel out the $(x - 6)$ terms.
The limit simplifies to $\lim_{x
ightarrow6}\frac{x + 5}{8}$.

Step3: Substitute the value of $x$

Substitute $x = 6$ into $\frac{x+5}{8}$.
We get $\frac{6 + 5}{8}=\frac{11}{8}$.

Answer:

$\frac{11}{8}$