# Thread: [SOLVED] Limit

1. ## [SOLVED] Limit

How do I get this answer?

2. $\cos x = 1-\frac{x^2}{2} + O(x^4)$. Alternatively, use l'Hopitals rule.

3. Originally Posted by Susaluda

How do I get this answer?
A lazy way is to use l'Hopital's Rule twice.

A not so lazy way is to substitute the power series for cos(2x) and cos(3x), simplify and then take the limit.

Another not so lazy way is to use the well known limit $\lim_{t \to 0} \frac{\cos (t) - 1}{t^2} = 1$.

4. it's actually $\frac{1-\cos t}{t^2}\to\frac12.$

5. Originally Posted by Krizalid
it's actually $\frac{1-\cos t}{t^2}\to\frac12.$
Thanks. Careless typos on my part.