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Y=xtanx/x^2+1 when is it discontinuous

for me it is always continuous because theres the +1 in the denominator, however the back of my book says that the answer is all x except npi/2

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Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
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x2+1 is never 0 if x is real.  However, tan x = sinx/cosx is undefined when x = ±π/2, ±3π/2, ...
So, the domain = {x l x ≠ ±π/2, ±3π/2, ...}
                      = {x l x ≠ nπ/2, where n is an odd integer}   


Emmanuel S. | Mathematics/Science TutorMathematics/Science Tutor
4.9 4.9 (152 lesson ratings) (152)
Hi, Pia,
You are correct in that the denominator x^2+1 doesn't become zero. However, tan(x)  can still be undefined. Remember that tan x = sin(x)/cos(x), so you need to determine when the cos x = 0. Recall from the unit circle that this would be when x = pi/2, 3pi/2, 5pi/2, etc. So the function would be discontinuous at those x values. I hope this helps. :)