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Math Help - continuity with limits!

  1. #1
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    continuity with limits!

    please be specific with answers...


    to prove that sine is continuous we need to show that limx--> sin(x)=sin(a) for every real number a. if we let h=x-a, then x=a+h and x-->a <--> h-->0. so an equivalent statement is that

    limh-->0sin(a+h) = sin(a)

    use the theorem:

    limx-->0cos(x) = 1 and limx-->0sin(x)=0

    to show that this is true.


    please help me with detailed steps!
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  2. #2
    MHF Contributor

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    Re: continuity with limits!

    No, you don't want someone to do this for you nor do you need it. The only thing you need to know is the "sum theorem": sin(x+h)= sin(x)cos(h)+ cos(x)sin(h)
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