求极限(e^cosx-e)/(x^2),x趋向于0

Question

求极限(e^cosx-e)/(x^2),x趋向于0

Answer 1

利用等价无穷小e^x-1~x,1-cosx~x²/2 (x->0)知
e^cosx-e=e[e^{cosx-1}-1}~e(cosx-1)~-ex²/2
所以原式=lim{x->0}(-ex²/2)/x²=-e/2