Questions: lim as x approaches 6 from the left of 5/(x-6) =

lim as x approaches 6 from the left of 5/(x-6) =
Transcript text: \(\lim _{x \rightarrow 6^{-}} \frac{5}{x-6}=\)
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Solution

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Solution Steps

To find the limit of the function as \( x \) approaches 6 from the left, we need to analyze the behavior of the function \( \frac{5}{x-6} \). As \( x \) gets closer to 6 from the left, \( x-6 \) becomes a very small negative number, causing the fraction to approach negative infinity.

Step 1: Analyze the Function Behavior

Consider the function \( f(x) = \frac{5}{x-6} \). We are interested in the behavior of this function as \( x \) approaches 6 from the left (\( x \to 6^{-} \)).

Step 2: Evaluate the Limit

As \( x \) approaches 6 from the left, the expression \( x-6 \) becomes a very small negative number. Consequently, the fraction \( \frac{5}{x-6} \) becomes very large in the negative direction.

Step 3: Determine the Limit

The limit of the function as \( x \) approaches 6 from the left is: \[ \lim_{x \to 6^{-}} \frac{5}{x-6} = -\infty \]

Final Answer

\(\boxed{-\infty}\)

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