Question

Let f(x) = [(lncosx/(4√(1 + x²) - 1), if x > 0), ((e^sin4x - 1)/(ln(1 + tan2x)), if x < 0) is it possible to define f(0) to make the function continuous at x = 0. If yes what is the value of f(0), if not then indicate the nature of discontinuity.

Answer 1

[f(0⁺) = - 2]

hence f(0) can not define. and 

∴ f(0^-) & f(0⁺) are finite hence there non-removable type discontinuity.