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Math Help - Trigo-limit

  1. #1
    Super Member dhiab's Avatar
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    Trigo-limit

    Calculate :

    LIM ( 9x + sin(x))/(x sec(x))
    x---> 0
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Quote Originally Posted by dhiab View Post
    Calculate :

    LIM ( 9x + sin(x))/(x sec(x))
    x---> 0
    \lim_{x \to 0} \frac{9x+\sin(x)}{x\sec(x)}

    \lim_{x \to 0} \left(\frac{9x}{x\sec(x)}+\frac{\sin(x)}{x\sec(x)}  \right)

    \lim_{x \to 0} \left(\frac{9}{\sec(x)}+\frac{\sin(x)}{x}\frac{1}{  \sec(x)}\right)

    Now consider

    \lim_{x \to 0} \frac{\sin(x)}{x}=1

    does this help?
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  3. #3
    Senior Member DeMath's Avatar
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    Quote Originally Posted by dhiab View Post
    Calculate :

    LIM ( 9x + sin(x))/(x sec(x))
    x---> 0
    \mathop {\lim }\limits_{x \to 0} \frac{{9x + \sin x}}<br />
{{x\sec x}} = \mathop {\lim }\limits_{x \to 0} \frac{{\cos x\left( {9x + \sin x} \right)}}<br />
{x} =

    = \mathop {\lim }\limits_{x \to 0} \left( {9\cos x + \cos x \cdot \frac{{\sin x}}{x}} \right) =

    = 9\mathop {\lim }\limits_{x \to 0} \cos x + \mathop {\lim }\limits_{x \to 0} \cos x \cdot \mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}<br />
{x} =
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