lim x-0 1-cosx / x^2=1/2?
2024-02-11 10:27
用恒等变形怎么推呢
匿名用户
2024-02-11 12:11
1-cosx =1-[1-2sin²(x/2)]=2sin²(x/2)
当x→0时，sin²(x/2) ～ x/2
则
1-cosx ～ x²/2
即
lim x-0 1-cosx / x^2=1/2
当x→0时，sin²(x/2) ～ x/2
则
1-cosx ～ x²/2
即
lim x-0 1-cosx / x^2=1/2
更多回答
lim(x→0) (1-cosx)/x^2
=lim(x→0) 2sin^2(x/2)/x^2 sinx~x 那么sin(x/2)~x/2 (x→0)
=lim(x→0) 2*(x/2)^2/x^2
=1/2
=lim(x→0) 2sin^2(x/2)/x^2 sinx~x 那么sin(x/2)~x/2 (x→0)
=lim(x→0) 2*(x/2)^2/x^2
=1/2
