Find the discontinuities of the function and prove that these discontinuities exist.

Question

f(x) = (x^2)(tanx)

Answer 1

The discontinuities come from tan(x). Tan(90°)=tan(π/2) is undefined, likewise any odd integer multiple of this, so this where the discontinuity lies. Any expression involving tan will be affected. So x=(2n+1)π/2, where n is any integer, is where the discontinuities occur.