find the limit. write ∞ or - ∞ where appropriate.\nlim(x→1) - 4/(x - 1)^2\nlim(x→1) - 4/(x - 1)^2 =…

find the limit. write ∞ or - ∞ where appropriate.\nlim(x→1) - 4/(x - 1)^2\nlim(x→1) - 4/(x - 1)^2 = (simplify your answer.)

find the limit. write ∞ or - ∞ where appropriate.\nlim(x→1) - 4/(x - 1)^2\nlim(x→1) - 4/(x - 1)^2 = (simplify your answer.)

Answer

Explanation:

Step1: Analyze denominator behavior

As $x\to1$, $(x - 1)^2\to0$. And $(x - 1)^2>0$ for $x\neq1$.

Step2: Analyze the whole - fraction behavior

We have $\lim_{x\to1}\frac{-4}{(x - 1)^2}$. Since the numerator is a non - zero negative constant $(-4)$ and the denominator $(x - 1)^2$ approaches $0$ from the positive side as $x\to1$. The fraction $\frac{-4}{(x - 1)^2}\to-\infty$.

Answer:

$-\infty$