# $\lim_{x\to0}\frac{\sin x-x}{x^3}$ without de l'Hospital's Rule? [duplicate]

I know, how to calculate $$\lim_{x\to0}\frac{\cos x-1}{x^2}$$ without differential calculus. Calculating $$\lim_{x\to0}\frac{\sin x-x}{x^3}$$ using de l'Hospital's rule or Taylor expansion is also easy.

Is there a method to calculate the previous limit without de l'Hospital's rule or stronger tools?

• The solution is provided by the second answer (user17762's one) given here: math.stackexchange.com/questions/134051/… – Marco Vergura Dec 26 '14 at 11:14
• Thank you both! It is a trick I need. – Przemysław Scherwentke Dec 26 '14 at 11:18
• @PrzemysławScherwentke I see you have created new tag called (elementary-proof). It is recommended that a user who creates a new tag also creates tag-info - at least some basic info on the intended use of the new tag in the tag-excerpt. See, for example, this answer on meta. If some more details are needed, feel free to drop me a line in chat. – Martin Sleziak Dec 27 '14 at 10:06