# continuity

• Apr 14th 2010, 12:19 PM
sydewayzlocc
continuity
Im having trouble with this problem :

Consider the following. f(x)=tan(πx/2)

Find the x-values at which f is not continuous. Are these discontinuities removable? (Use k as an arbitrary integer. If an answer does not exist, enter DNE.)
• Apr 14th 2010, 01:08 PM
bigwave
Quote:

Originally Posted by sydewayzlocc
Im having trouble with this problem :

Consider the following. f(x)=tan(πx/2)

Find the x-values at which f is not continuous. Are these discontinuities removable? (Use k as an arbitrary integer. If an answer does not exist, enter DNE.)

functions are not continous where there is asymptotes

if you graph this you see that there are asymptotes k distance apart

hope this helps
• Apr 14th 2010, 02:48 PM
sydewayzlocc
can you explain that a little more?
• Apr 14th 2010, 02:54 PM
skeeter
Quote:

Originally Posted by sydewayzlocc
can you explain that a little more?

tan(odd multiples of pi/2) is undefined
• Apr 14th 2010, 03:08 PM
sydewayzlocc
im still confused as to how to answer this, i know that its undefined at odd multiples of pi/2 but how do i write that as a value of x?
• Apr 14th 2010, 03:22 PM
skeeter
Quote:

Originally Posted by sydewayzlocc
im still confused as to how to answer this, i know that its undefined at odd multiples of pi/2 but how do i write that as a value of x?

$\displaystyle x = 2k+1 \, , \, x \in \mathbb{Z}$