Question

Consider the following.
\(\Large f(x) = tan\left(\frac{\pi x }{2}\right)\)
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.)
http://prntscr.com/ccqre4

Answer 1

Consider the following.
\(\Large f(x) = tan\left(\frac{\pi x }{2}\right)\)
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.)
http://prntscr.com/ccqre4

So, I tried 2k first and then 1/2k both of which are wrong :x

Answer 2

tan(x) has a removable discontinuity at pi/2k

so tan(pi*x/2) has a removable discontinuity at k

no, that's also wrong >.<

Answer 3

x=2k+1,where k is an integer.

Answer 4

yeah!!

Answer 5

Considered.

Answer 6

How did you arrive at x = 2k + 1?

That was correct, but I need to learn this more than get it right xD

Answer 7

odd multiple of pi/2

Answer 8

I don't quite follow

Answer 9

for all k in Z, 2k+1 is an odd number, right?
like k =0, then 2k+1=1 odd
k=1, 2k+1=3 odd
k=2, 2k+1=5 odd
so on
and with odd number, you have tan ((pi/2)* odd ) undefined. dat sit

Answer 10

Ohhhh, I see

Because the discontinuity wasn't at 1, 2, 3, ...

It was at 1, 3, 5, 7

Ahh, I see where I was going wrong now!

Thanks all! :)

Answer 11

\[tanx=\frac{ \sin x }{ \cos x },if \cos x=0\]
it is undefined.
x=pi/2,3 pi/2,....

Answer 12

Yes, I see now. Thanks! :)

Answer 13

yw.