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Math Help - Limits using trig functions

  1. #1
    Junior Member Cyberman86's Avatar
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    Limits using trig functions

    I got stuck on this one, once i saw the sin, i just didn't know what to do. All this is one problem. The Answer according to the book is Cos(x)

    f(x) = sin(x)

    f(x) = lim sin(x+h) - sin (x) over h
    ........h->0
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Cyberman86 View Post
    I got stuck on this one, once i saw the sin, i just didn't know what to do. All this is one problem. The Answer according to the book is Cos(x)

    f(x) = sin(x)

    f(x) = lim sin(x+h) - sin (x) over h
    ........h->0
    You're expected to recognise the limit as the derivative of sin x (calculated from first principles).
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  3. #3
    Super Member Showcase_22's Avatar
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    Interesting, let me give this a bash:

    \frac{f(x+h)-f(x)}{h}=\frac{sin(x+h)-sin x}{h}

    \frac{sin x cos h+sin h cos x-sinx}{h}

    as h---->0:

    sin h\rightarrow h \, and  \, cos h\rightarrow 1

    \frac{sin x+hcos x-sinx}{h}

    \frac{hcos x}{h}

    =cosx
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