EXAMPLE 6 The Heaviside function H is defined by
H(t) = {(0 text( if ) t < 0,1 text( if ) t >= 0)
[This function is named after the electrical engineer Oliver Heaviside (1850-1925) and can be used to describe an electric current that is switched on at time t = 0.] Its graph is shown in the figure.
As t approaches 0 from the left, H(t) approaches
. As t approaches 0 from the right, H(t) approaches . Therefore the limit as t approaches 0 of H(t) does not exist.