# limits help part 2

• Oct 1st 2012, 05:49 PM
ubhutto
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)
• Oct 1st 2012, 05:57 PM
Prove It
Re: limits help part 2
Quote:

Originally Posted by ubhutto
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*}.