7. -/3.84 points evaluate the limit, if it exists. (if an answer does not exist, enter dne.)…
7. -/3.84 points evaluate the limit, if it exists. (if an answer does not exist, enter dne.) $lim_{x\rightarrow1}\frac{x^{2}-4x + 3}{x - 1}$
Answer
Explanation:
Step1: Factor the numerator
Factor $x^{2}-4x + 3$ as $(x - 1)(x - 3)$. So the limit becomes $\lim_{x\rightarrow1}\frac{(x - 1)(x - 3)}{x - 1}$.
Step2: Simplify the function
Cancel out the common factor $(x - 1)$ (since $x\neq1$ when taking the limit). We get $\lim_{x\rightarrow1}(x - 3)$.
Step3: Evaluate the limit
Substitute $x = 1$ into $x-3$. So $1-3=-2$.
Answer:
$-2$