Question

For the function f=csc(pi x/6) for abs(x-3)<=2
and 2 for abs(x-3)>2,
Find the discontinuities anmd state if they are removeable.

Answer 1

Oh boy, these intervals are kind of tricky :o(

Answer 2

Agreed

Answer 3

Sorry I was at school before D: That keyboard is so hard to type on...

Answer 4

\[\Large\rm \left|x-3\right|\le2\]We can write this as:\[\Large\rm \cases{~~\quad x-3~\le2\\ \rm -(x-3)\le2}\]Solving for x in each case,\[\Large\rm \cases{x\le5\\ \rm x\ge1}\]

Answer 5

Which can be written as \(\Large\rm 1\le x\le5\)

Answer 6

Here is our function,
\[\Large\rm f(x)=\cases{\csc\left(\frac{\pi x}{6}\right), &$1\le x\le5$\\ \rm 2, &$\left|x-3\right|\gt2$}\]Understand how I rewrote the interval for the first part?

Answer 7

We'll need to do the same thing for the other part.