Question

attempt 2: 1 attempt remaining. evaluate the limit (lim_{x \to -5} |x + 5|) enter inf for (infty), -inf for (-infty), and dne if the limit does not exist. limit = submit answer next item

Explanation:

Step1: Recall the definition of absolute value function

The absolute value function \(|f(x)|\) is continuous everywhere where \(f(x)\) is continuous. Here, \(f(x)=x + 5\) is a linear function, hence continuous everywhere.

Step2: Evaluate the limit by direct substitution

For a continuous function \(y = f(x)\) at \(x=a\), \(\lim_{x
ightarrow a}f(x)=f(a)\). So, for \(\lim_{x
ightarrow - 5}|x + 5|\), we substitute \(x=-5\) into \(|x + 5|\).
Substituting \(x=-5\) gives \(|-5 + 5|=|0| = 0\).

Answer:

\(0\)