Question

lim[(1-cosX)/x的平方]是多少,X趋近于0时

Answer 1

1- cosX = 1 - [ 1 - 2(sinx/2)^2] = 2[sin(x/2)]^2

1-cosX/X^2 = 2[sin(x/2)]^2/x^2

= (1/2)* [sin(x/2)/(x/2)]^2

sin(x/2)/(x/2) 当x趋近于0时,其极限为1

（这是书上的基本定理）

因此

lim[(1-cosX)/x^2] = 1/2