Questions: Determine the infinite limit. lim as x approaches -5 from the right of (x+6)/(x+5) ∞ -∞

Solution Steps

To determine the infinite limit as $x$ approaches $-5$ from the right, we need to analyze the behavior of the function $\frac{x+6}{x+5}$ as $x$ gets closer to $-5$ from values greater than $-5$. Specifically, we should look at the numerator and the denominator separately to understand how the function behaves near this point.

We are given the function: $$f(x) = \frac{x+6}{x+5}$$ We need to find the limit as $x$ approaches $-5$ from the right: $$\lim_{x \to -5^+} \frac{x+6}{x+5}$$

As $x$ approaches $-5$ from the right ($x \to -5^+$):

• The numerator $x + 6$ approaches $-5 + 6 = 1$.
• The denominator $x + 5$ approaches $-5 + 5 = 0$ from the positive side.

Since the numerator approaches a positive value (1) and the denominator approaches zero from the positive side, the fraction $\frac{x+6}{x+5}$ will grow without bound in the positive direction.

Final Answer