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Math Help - trigonometric limits

  1. #1
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    trigonometric limits

    Hey guys im new here, but I have a test today and I need to understand trig limits better.

    lim of x approaching 0
    sin(4x)
    sin(6x)

    the hint that was given was "use the identity Lim x approaching 0
    sinx = 1"
    x
    Last edited by fortplainman; October 8th 2008 at 05:45 AM.
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  2. #2
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    oh and another question, which is on the def. of a derivitive, i just cannot remember the equation of a tangent line/equation of the normal line.
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  3. #3
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    Multiply by \frac{x}{x}, so that you would get:

    \frac{\sin{4x}}{x} \cdot \frac{x}{\sin{3x}}

    What's left is simple manipulation to get your limit into something like sin(u)/u
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  4. #4
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    Quote Originally Posted by fortplainman View Post
    oh and another question, which is on the def. of a derivitive, i just cannot remember the equation of a tangent line/equation of the normal line.
    The derivative is the slope of the tangent line. The equation of a line in point slope form is given by:

    y - y_1 = m(x-x_1)

    Where (x_1, y_1) is the point in question and m is the slope. The equation of the normal line to this line contains (x_1, y_1), but its slope is the negative reciprocal of the original line.

    For instance, if line K has a slope of 4, then the line that is perpendicular/normal to line k will have a slope of -\frac{1}{4}. Just remember that:

    m_{line} \cdot m_{normal} = -1
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  5. #5
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    oh ok I thought i was right on the tangent equation, but thanks for the normal info and hopefully the trig limit info will help me out. thanks.
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  6. #6
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    Quote Originally Posted by Chop Suey View Post
    Multiply by \frac{x}{x}, so that you would get:

    \frac{\sin{4x}}{x} \cdot \frac{x}{\sin{3x}}

    What's left is simple manipulation to get your limit into something like sin(u)/u
    would this still work with if the question were to be:
    sin2x
    x
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  7. #7
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    \frac{{\sin (4x)}}<br />
{{\sin (6x)}} = \left( {\frac{4}<br />
{6}} \right)\left( {\frac{{\frac{{\sin (4x)}}<br />
{{4x}}}}<br />
{{\frac{{\sin (6x)}}<br />
{{6x}}}}} \right)
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