question 24 (1 point) find the limit algebraically. you must show work in order to receive credit! lim(x→4)…
question 24 (1 point) find the limit algebraically. you must show work in order to receive credit! lim(x→4) (x - 4)/(x² - 5x + 4)
Answer
Explanation:
Step1: Factor the denominator
Factor $x^{2}-5x + 4$ as $(x - 4)(x - 1)$. So the limit becomes $\lim_{x\rightarrow4}\frac{x - 4}{(x - 4)(x - 1)}$.
Step2: Simplify the fraction
Cancel out the common factor $(x - 4)$ (since $x\neq4$ when taking the limit), we get $\lim_{x\rightarrow4}\frac{1}{x - 1}$.
Step3: Substitute the value of x
Substitute $x = 4$ into $\frac{1}{x - 1}$, we have $\frac{1}{4-1}=\frac{1}{3}$.
Answer:
$\frac{1}{3}$