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Math Help - Limit of Trig Function

  1. #1
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    Limit of Trig Function

    Find the limit of (sin x)/x as x--> 0
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by magentarita View Post
    Find the limit of (sin x)/x as x--> 0
    Without knowing L'Hopital's Rule, one can show this is the case using the Squeeze Theorem. You can find a proof here.
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    Like a stone-audioslave ADARSH's Avatar
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    For simplicity
    sinx can be expanded as
     x -\frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}........


    So the Limit now becomes
     <br />
Lim_{x->0} \frac{x -\frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}........}{x}<br /> <br />

     <br />
= Lim_{x->0} {1 -\frac{x^3}{x*3!} + \frac{x^5}{x*5!} - \frac{x^7}{x*7!}........}<br /> <br />
     <br />
= 1<br />

    Its better if you follow Chris
    Last edited by Krizalid; February 9th 2009 at 01:49 AM.
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  4. #4
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    Thanks but.......

    Thank you but I am still a little lost here.
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  5. #5
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    magentarita's not ready to diggest ADARSH's post since he/she's covering limits.

    But, follow Chris L T521's link, which provides a geometric proof.
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  6. #6
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    yes but.........

    Quote Originally Posted by Krizalid View Post
    magentarita's not ready to diggest ADARSH's post since he/she's covering limits.

    But, follow Chris L T521's link, which provides a geometric proof.
    You are right but this is the main reason why I post questions here---to learn, that it.
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  7. #7
    Moo
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    Or you can use the definition of the derivative :

    \lim_{x \to 0} \frac{f(a+x)-f(a)}{x}=f'(a)

    let f be the sine function, and a=0, remember that the derivative of the sine function is cosine, and observe


    I guess this method suits the most what you're currently doing...
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  8. #8
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    Quote Originally Posted by Moo View Post
    Or you can use the definition of the derivative :

    \lim_{x \to 0} \frac{f(a+x)-f(a)}{x}=f'(a)

    let f be the sine function, and a=0, remember that the derivative of the sine function is cosine, and observe
    How do you think the derivative of sine is derived in the first place!
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