Question

question 6 - 1 point write the following sentence regarding a limit symbolically. provide the explicit expression for the given function. the limit of the function f(x)= - 4/(x + 5)^2 as x approaches - 5 is negative infinity. provide your answer below: lim_(x→□)□=-□

Explanation:

Step1: Analyze the denominator behavior

As $x\to - \infty$, $(x + 5)^2=(x+5)(x + 5)$. When $x\to-\infty$, both $(x + 5)$ factors approach $-\infty$, and their product $(x + 5)^2\to+\infty$.

Step2: Analyze the whole - function limit

We have the function $f(x)=-\frac{4}{(x + 5)^2}$. Since the denominator $(x + 5)^2\to+\infty$ as $x\to-\infty$ and the numerator is a non - zero constant $-4$, then $\lim_{x\to-\infty}-\frac{4}{(x + 5)^2}=0$.

Answer:

$0$