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Math Help - limits help part 2

  1. #1
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    limits help part 2

    i got one more limit problem that i cannot figure out

    (x^2 sin x) / (1 - cos^2x) x is 0

    how do i prove this

    PS i got to the part (x^2 / sinx)

    but i dont know how to convert it into sin(x) / (x)
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  2. #2
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    Re: limits help part 2

    Quote Originally Posted by ubhutto View Post
    i got one more limit problem that i cannot figure out

    (x^2 sin x) / (1 - cos^2x) x is 0

    how do i prove this

    PS i got to the part (x^2 / sinx)

    but i dont know how to convert it into sin(x) / (x)
    Write it as \displaystyle \begin{align*} x \cdot \frac{x}{\sin{x}} \end{align*}. Since \displaystyle \begin{align*} \lim_{x \to 0} \frac{\sin{x}}{x} = 1 \end{align*}, so does \displaystyle \begin{align*} \lim_{x \to 0}\frac{x}{\sin{x}} \end{align*}. The reason is that for very small values of x, \displaystyle \begin{align*} \sin{x} \approx x \end{align*}.
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