I'm trying to find the left, right, and overall limits of this function without using a calculator. Any help/suggestions on how I'm supposed to do this would be very helpful!

Question

f(x){ sinx if x<pi/6
tanx if x=pi/6 a=pi/6
cosx if x>pi/6

Answer 1

left limit is 1/2
f(pi/6) = 1/√3
right limit is √3/2

So, not only are the left and right limits different, but even if they were the same, f(x) is defined to be something else at x=pi/6!