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Math Help - Calc Problem

  1. #1
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    Calc Problem

    The function f is defined by


    f(x)=
    (sinx)/(x) , x ≠ 0

    1, x=0


    A) at what points does its graph cross the x-axis?
    B) What is the relation between x and tanx at points x≠0 at which f'(x)=0
    C)What is the behavior of f as the absolute value of x approaches infinite
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  2. #2
    Eater of Worlds
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    A: \frac{sin(x)}{x}=0

    x=C{\pi}

    B: f'(x)=\frac{cos(x)}{x}-\frac{sin(x)}{x^{2}}

    \frac{cos(x)}{x}=\frac{sin(x)}{x^{2}}

    x^{2}cos(x)=xsin(x)

    x=\frac{sin(x)}{cos(x)}=tan(x)

    C:

    \lim_{x\to {\infty}}\frac{sin|x|}{|x|}

    \lim_{x\to {\infty}}\frac{sin(-x)}{-x}=\lim_{x\to {\infty}}\frac{-sin(x)}{-x}=\lim_{x\to {\infty}}\frac{sin(x)}{x}

    See the limit?.
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    sry, just to clarify, <br />
\lim_{x\to {\infty}}\frac{sin|x|}{|x|}<br />
is the same as <br />
\lim_{x\to {\infty}}\frac{sinx}{x}<br />
which is zero, correct?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    sry, just to clarify, <br />
\lim_{x\to {\infty}}\frac{sin|x|}{|x|}<br />
is the same as <br />
\lim_{x\to {\infty}}\frac{sinx}{x}<br />
which is zero, correct?
    yes. since |x| = x when x is positive. and the limit goes to zero. you can prove this using the squeeze theorem. one of many ways
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