# Thread: Find convergence by using taylor series

1. ## Find convergence by using taylor series

$\lim_{x\to 0}\frac{cosx-cos(3x)}{sin(x^2)}$

I'm having trouble finding things to cancel out to get the right answer.

and also

$si(x)=\int_{0}^{x} \frac{sin(t)dt}{t}$

$\lim_{x\to 0} \frac{si(x)-x}{x^3}$

Same thing

2. Do you have to use taylor series, or can you use other methods?

3. My professor said do by series