Thanks for your answers, I'm sorry for responding so late. calculusfunctions, why does \[\lim_{x \rightarrow 0}\frac{ \sin x }{ \cos x + 1 } = (1)(0)\]
and how do we proof, that \[\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1\]
nickfrei, thanks for the proofs of limits, but unfortunately I haven't taken the mathematical analysis course yet, so I still fill a bit uncomfortable with it's theorems (actually, I've used a wrong textbook to learn it and failed...).