Question

homework 1.2: limits involving infinity
score: 25/36 answered: 15/18
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question 16
0/2 pts 8 49 details
evaluate the limit
\\(\lim_{x\to6}\frac{-3x + 18}{x^{2}-14x + 48}=\\)
question help: video 1 video 2 written example 1
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Explanation:

Step1: Factor the numerator and denominator

The numerator \(-3x + 18=-3(x - 6)\). The denominator \(x^{2}-14x + 48=(x - 6)(x - 8)\)
So the function becomes \(\lim_{x
ightarrow6}\frac{-3(x - 6)}{(x - 6)(x - 8)}\)

Step2: Simplify the function

Cancel out the common factor \((x - 6)\) (since \(x
eq6\) when taking the limit), we get \(\lim_{x
ightarrow6}\frac{-3}{x - 8}\)

Step3: Substitute \(x = 6\)

Substitute \(x=6\) into \(\frac{-3}{x - 8}\), we have \(\frac{-3}{6 - 8}=\frac{-3}{-2}=\frac{3}{2}\)

Answer:

\(\frac{3}{2}\)