Question

answer the following true or false: if lim_{x→4} f(x)= - 2 then f(x) is continuous at x = 4. true false question help: message instructor submit question jump to answer

Explanation:

Step1: Recall continuity condition

For a function $f(x)$ to be continuous at $x = a$, three conditions must be met: 1. $\lim_{x
ightarrow a}f(x)$ exists, 2. $f(a)$ is defined, 3. $\lim_{x
ightarrow a}f(x)=f(a)$. Just knowing $\lim_{x
ightarrow 4}f(x)= - 2$ does not tell us if $f(4)$ is defined or if $\lim_{x
ightarrow 4}f(x)=f(4)$.

Answer:

False