Question

find the limit. write ∞ or - ∞ where appropriate.
lim(x→5⁻) 3/(x - 5)
lim(x→5⁻) 3/(x - 5)= (simplify your answer.)

Explanation:

Step1: Analyze the denominator

As $x\to5^{-}$, we consider values of $x$ that are less than 5 but approaching 5. So, $x - 5\to0^{-}$.

Step2: Analyze the fraction

We have the fraction $\frac{3}{x - 5}$. Since the numerator is a non - zero constant 3 and the denominator is approaching 0 from the negative side, $\frac{3}{x - 5}\to-\infty$.

Answer:

$-\infty$