Questions: Determine the infinite limit. lim x -> -8^- (x+7)/(x+8) ∞ -∞

Transcript text: Detérmine the infinite limit. \[ \lim _{x \rightarrow-8^{-}} \frac{x+7}{x+8} \] $\infty$ $-\infty$

Solution

Solution Steps

To determine the infinite limit as $ x $ approaches $-8$ from the left for the function $\frac{x+7}{x+8}$, we need to analyze the behavior of the numerator and the denominator. As $ x $ approaches $-8$ from the left, the numerator $ x+7 $ approaches $-1$ and the denominator $ x+8 $ approaches $0$ from the negative side. This will result in a large positive value.

Step 1: Analyze the Function as $ x $ Approaches $-8$ from the Left

We need to determine the limit of the function $ \frac{x+7}{x+8} $ as $ x $ approaches $-8$ from the left.

Step 2: Behavior of the Numerator and Denominator

As $ x $ approaches $-8$ from the left:

The numerator $ x + 7 $ approaches $-1$.
The denominator $ x + 8 $ approaches $0$ from the negative side.

Step 3: Determine the Limit

Since the numerator is a constant $-1$ and the denominator approaches $0$ from the negative side, the fraction $ \frac{x+7}{x+8} $ will approach $ +\infty $.

Final Answer

$\boxed{\infty}$

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