# Discontinuous split function problem

1. Sep 21, 2004

### ucdawg12

im not really sure how to do this one because I have forgotten most of the things about trig functions from last year, but here is the problem:
(im going to say Ħ=pi because I cant find the character for pi)
f(x)= tan((Ħx)/4) when |x|<1
x when |x| =>(greater than or equal to) 1

Im supposed to find the x values, if any, at which f is not continuous, and find which of the discontinuities are removable.

I havent had a lot of problems with my split function questions, I just dont know how to handle it when trig functions are involved, can anyone explain?

Thanks

2. Sep 21, 2004

### HallsofIvy

Staff Emeritus
First of all, you can create a π by using & p i ; but without the spaces- it doesn't look like a very good "pi" to me- the other Greek letters using & ...; are better!

Secondly, the way to handle a "piece-wise" function (what you are calling a "split" function) is to look at the individual "pieces" and then look carefully at the point where they meet.

-1< x< 1 f(x)= tan(π x) Okay, where is tan(π x) NOT continuous. That's really the same as asking "where is tan(&pi x) not defined. All "elementary" functions are continuous wherever they are defined.

For x< -1 or x> 1, f(x)= 1. That's easy, that's a constant and so it is always defined and always constant.

Now, what about x= -1 or x= 1? as x-> 1, πx-> &pi. What is the value of tan(π)? As x-> 1, 0-> 0, of course, so that limit is 0. IF limit tan(πx)= tan(π)= 0 then the function is continous at x= 1.

As x-> -1, π x-> -&pi. What is the value of tan(-π)? As x-> 0 0-> 0, of course, so that limit is 0. IF limit tan(-πx)= tan(π)= 0, then the function is continous at x= -1.