[SOLVED] Evaluation of a limit

**sinewave85** · February 24th 2009, 12:56 PM

Could someone explain to me how to properly evaluate the limit of this equation:

$\frac{x^2}{1 - \cos{x}}$

as x approaches 0 from the right? I know that the answer is 2 from testing values close to 0, but that won't be good enough for full credit.

**Danny** · February 24th 2009, 01:14 PM

Originally Posted by sinewave85

Could someone explain to me how to properly evaluate the limit of this equation:

$\frac{x^2}{1 - \cos{x}}$

as x approaches 0 from the right? I know that the answer is 2 from testing values close to 0, but that won't be good enough for full credit.

$\frac{x^2}{1 - \cos x} = \frac{x^2}{1 - \cos x} \frac{1 + \cos x }{1 + \cos x } = \frac{x^2(1 + \cos x)}{1 - \cos^2 x } = \frac{x^2}{\sin^2 x }(1 + \cos x)$ Now do the separate limits.

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