jwilliams2234 jwilliams2234
  • 23-03-2022
  • Mathematics
contestada

List the discontinuities for the function f(x) = cot( 5x/3 ).

Respuesta :

goddessboi goddessboi
  • 23-03-2022

Answer:

[tex]x=\frac{3\pi n}{5}[/tex]

Step-by-step explanation:

We know that [tex]cot(\frac{5x}{3})=\frac{cos(\frac{5x}{3})}{sin(\frac{5x}{3})}[/tex], so [tex]cot(\frac{5x}{3})[/tex] is undefined where [tex]sin(\frac{5x}{3})=0[/tex]:

[tex]sin(\frac{5x}{3})=0\\\\\frac{5x}{3}=\pi n\\\\5x=3\pi n\\\\x=\frac{3\pi n}{5}[/tex]

So, the discontinuities for the function [tex]f(x)=cot(\frac{5x}{3})[/tex] are where [tex]x=\frac{3\pi n}{5}[/tex] with [tex]n[/tex] being any integer.

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