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Math Help - Show that sin(x) is continuous

  1. #1
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    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.
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  2. #2
    MHF Contributor Siron's Avatar
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    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)?
    Thanks from mathlearner100
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    Re: Show that sin(x) is continuous

    I will try, thank you.
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    MHF Contributor Siron's Avatar
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    Re: Show that sin(x) is continuous

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