Using the continuity concept, it is found that the function that is continuous at x = 18 is given by:
[tex]f(x) = \frac{(x - 18)^2}{x}[/tex]
What is the continuity concept?
A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem:
- In the first function, all these characteristics are respected, hence, the function is continuous.
- For the second function, x = 18 is zero of the denominator, hence the function is not defined at x = 18.
- For the third function, the tangent is not defined at [tex]0.5\pi[/tex], as [tex]\cos{0.5\pi} = 9[/tex], hence the function is not defined at x = 18.
In the fourth function:
[tex]f(18) = 36[/tex]
[tex]\lim_{x \rightarrow 18^-} f(x) = 18^2 \neq 36[/tex]
Hence also not continuous.
You can learn more about the continuity concept at https://brainly.com/question/24637240
