Question

还有一道 limx→0 (1-cosx)/x^2

晕哦...明显是求极限,你说答案是多少就OK,简单的说就是化简以后求极限,要把分母的X^2=0变成其他因式,我忘了怎么做了..

Answer 1

x趋于零时,1-cosx等价于x^2/2,直接就可得出答案是1/2,这是考研的送分题呀！再说明白点,1-cosx=1-(1-2(sin(x/2))^2)=2sin(x/2)^2等价于x^2/2.老兄,我是考研科班出身的,分给我吧!

Answer 2

x→0，也就是说分子分母都会趋于0。所以把分子分母先求导再取极限。

Answer 3

我告诉你一招，在遇到0/0的类型求极限，可以直接求其分子与分母导数的商的极限，因而可以写成：lim (1-cosx)/x^2 x→0
=lim sinx/2x =lim sinx/x /2=1/2
x→0 x→0

Answer 4

化为limlimx→0 1/2[sin(x/2)/(x/2)]^2=1/2

Answer 5

limx→0 (1-cosx)/x^2
=lim (2sin^2 x/2) /x^2
=1/2 lim (sin^2 x/2)/(x/2)^2
=1/2 lim [(sinx/2)/(x/2)]^2
=1/2 * 1^2
=1/2

lim (sinx)/x=1
x->0