Question

homework 1.2: limits involving infinity
score: 19/36 answered: 12/18
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question 13
0/2 pts 8 49 details
evaluate the limit:
lim(x→7) (1x - 7)/(x² - 9x + 14) =

Explanation:

Step1: Factor the denominator

Factor $x^{2}-9x + 14=(x - 7)(x - 2)$. So the limit becomes $\lim_{x
ightarrow7}\frac{x - 7}{(x - 7)(x - 2)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 7)$ (for $x
eq7$). We get $\lim_{x
ightarrow7}\frac{1}{x - 2}$.

Step3: Substitute the value of $x$

Substitute $x = 7$ into $\frac{1}{x - 2}$. We have $\frac{1}{7-2}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$