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Which function is continuous at X equals 18

Which Function Is Continuous At X Equals 18 class=

Sagot :

Answer: A

Step-by-step explanation:

pretty sure :)

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

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