# Find the values at which the function fails to be continuous (trig)

• Sep 6th 2010, 02:56 PM
yzobel
Find the values at which the function fails to be continuous (trig)
find all the values of x at which the function fails to be continuous
f(x)= 2/(1+cos2x)

I believe the function fails to be continuous when the denominator equals zero(right?)
So wouldn't the correct answer be 2n(pi)+(pi/2) for all integers n? The answer keeps coming up as incorrect.

Could someone please correct me if I'm wrong?
Thank you! I appreciate the help!
• Sep 6th 2010, 03:23 PM
skeeter
Quote:

Originally Posted by yzobel
find all the values of x at which the function fails to be continuous
f(x)= 2/(1+cos2x)

I believe the function fails to be continuous when the denominator equals zero(right?)
So wouldn't the correct answer be 2n(pi)+(pi/2) for all integers n? The answer keeps coming up as incorrect.

Could someone please correct me if I'm wrong?
Thank you! I appreciate the help!

If the denominator is $\displaystyle 1 + \cos(2x)$ , then this function is discontinuous when

$\displaystyle 2x = \pm \pi , \pm 3\pi , \pm 5\pi , ...$

$\displaystyle x = \frac{\pi}{2} + k\pi \, ; \, k \in \mathbb{Z}$