Thread: Show that sin(x) is continuous

1. Show that sin(x) is continuous

Using the observation that the absolute value of sin(x) is less than or equal to the absolute value of x, show that sin(x) is continuous in x = 0.

2. Re: Show that sin(x) is continuous

You probably want an $\epsilon-\delta$ proof.
$\forall \epsilon>0, \exists \delta>0, \forall x \in \mathbb{R}: |x|<\delta \Rightarrow |\sin(x)|<\epsilon$
Can you proof the above statement (with the given hint)?

3. Re: Show that sin(x) is continuous

I will try, thank you.

4. Re: Show that sin(x) is continuous

Originally Posted by mathlearner100
I will try, thank you.
Great. With the hint the statement is proved immediately.