Question

prove signum function is continuous at x = 1​

Answer 1

Step-by-step explanation:

Signum function is an integer valued function defined over R . ... sgn(x) = 1, if x > 0 ; sgn(x) = 0, if x = 0 and sgn(x) = - 1, if x < 0 . Therefore, clearly, we have ; lim(x →0+) = 1 but lim(x→0-) = -1, so limit does not exist at x = 0 hence no question arise of its being continuous at x= 0 .