is there a method (arithmetic simplification or something) which with i can solve lim that combine ln, e, and trigonometry? for example:$\displaystyle lim_{x\rightarrow0}\frac{ln(cosx)}{cosx-1} $ and:

$\displaystyle lim_{x\rightarrow\infty}\frac{2x-sin2x}{x^{2}+cos^{^{2}}x} $