# How do I explain that sin(1/x) is not continuous at x=0?

• How do I explain that sin(1/x) is not continuous at x=0?

... =\sin(1/x)$is not uniformly continuous? ... How do I go about proving$f(x)=\sin(1/x) ... I really appreciate the time you took to explain the way of ...
Positive: 37 %
... that function isn't continuous at x = 0. It's not even ... Sin(1/x) -Cos(1/x)/x At x =0 or rather we ... x\right)}{\sin\left(x\right)}[/math] How do I ...
Positive: 34 %

### More resources

Uniform Continuity 19.4 (a) We will ... By part (a), it is clear that f(x) = 1/x2 is not uniformly continuous on ... x −0 = lim x→0 x2 sin 1 x −0 x = lim
Positive: 37 %
Continuous Functions. A function is continuous when its graph is a single unbroken curve ... = 1/(x-1) for x>1: NOT continuous : ... At x=0 it has a very ...
Positive: 32 %
C. CONTINUITY AND DISCONTINUITY 1. ... (not even as ±∞). Though sin(1/x) ... x > 0, −1, x < 0 does not have a continuous derivative f ...