Question

Where are the asymptotes of f(x) = tan 4x from x = 0 to x = pi over two

Answer 1

The trick here is to use when the function f(y)=tan(y) = Infinity. We know that a tan(y) graph goes to infinity at y=pi/2, 3pi/2, 5pi/2, 7pi/2 etc... Here, instead of y we have 4x so we know that 4x=pi/2, 3pi/2, 5pi/2, 7pi/2 etc.... And then x=pi/8, 3pi/8, 5pi/8, 7pi/8. We see that that 5pi/8 is greater than pi/2. So the solutions are x= pi/8 and 3pi/8.