F X 0 When X Is Rational

I c is a nonzero rational number.

F x 0 when x is rational. Since lim x 0 f x 0 f 0 we conclude that f is continuous at x 0 however f is continuous for all nonzero real numbers c. Stack exchange network consists of 176 q a communities including stack overflow the largest most trusted online community for developers to learn share their knowledge and build their careers. The following graph shows the approximate value v t of subprime normally classified as risky mort. A rational function f x contains quadratic functions in both the numerator and denominator.

By the density of the irrationals there exists a sequence of irrational numbers x n which converges to c. By signing up you ll. Use the δ ε definition of the limit to prove that lim x a f x does not exist for any a 0. Use the δ ε definition of the limit to prove that lim x 0 f x 0.

However f x n 0. Also the function f x has a vertical asymptote at x 5 a single x intercept of 2 0 and f. Solution for if if x is rational f æ 1 0 if x is irrational prove that lim f x 0. We are integrating the function math f x 0 math for math x math rational and math 1 math for math x math irrational over the domain math 0 1 math.

Show that f is not continuous at any real number.