Question

1. -/3.84 points evaluate the limit, if it exists. (if an answer does not exist, enter dne.) $lim_{x

ightarrow1}\frac{x^{2}-4x + 3}{x - 1}$

Explanation:

Step1: Factor the numerator

Factor $x^{2}-4x + 3$ as $(x - 1)(x - 3)$. So the limit becomes $\lim_{x
ightarrow1}\frac{(x - 1)(x - 3)}{x - 1}$.

Step2: Simplify the function

Cancel out the common factor $(x - 1)$ (since $x
eq1$ when taking the limit). We get $\lim_{x
ightarrow1}(x - 3)$.

Step3: Evaluate the limit

Substitute $x = 1$ into $x-3$. So $1-3=-2$.

Answer:

$-2$