Well, to be continuous the limit must exist.Q2) Let f: [0, infinity), -> R be defined by
f(x) = x sin (1/x) when x>0
and f(x) = 0 when x = 0.
Figure out if 'f' is continuous and differentiable at x = 0.
Let's describe the interval where it is continuous.
If we have:
By the Squeezing Theorem:
And we can conclude that
So f is continuous on the entire real line.