> 数学 >
当x→0时,证明1-cos x~x^2/2
人气:321 ℃ 时间:2020-06-04 20:11:32
解答
证明:
lim(x→0) (1-cosx) /(x^2 /2)
=lim(x→0) 2(1-cosx) /(x^2)
=lim(x→0) 2*2(sinx/2)^2 /(x^2)
=lim(x→0) [sin(x/2) ]^2 / (x/2)^2 令t=x/2
=lim(t→0) (sin t / t)^2
=1
所以:
x→0,1-cos x^2/2
推荐
猜你喜欢
© 2024 79432.Com All Rights Reserved.
电脑版|手机版