1-2cosx除以(sin(x-π/3)) 当x趋向于π/3 求极限!还有ln(1+3x)除以x 当x趋向0时 求极限!回答我会加分的!
问题描述:
1-2cosx除以(sin(x-π/3)) 当x趋向于π/3 求极限!还有ln(1+3x)除以x 当x趋向0时 求极限!
回答我会加分的!
答
0/0型的极限可以对分子,分母求导完成
1-2cosx 的导数是 -2sinx
sin(x-π/3) 的导数是 cons(x-π/3)
-2*(√3/2) / 1 = √3
ln(1+3x)的导数是 3/(1+3x)
x的导数是1
x -> 0 极限为3
答
1.
lim (1-2cosx)/sin(x-π/3) (用洛必达法则分子分母同时求导)
=lim [(-2)*(-sinx)/cos(x-π/3)]
=lim 2sin(π/3)/cos0=√3
2.
lim ln(1+3x)/x (ln(1+3x)的等价无穷小即为3x)
=lim3x/x
=3
答
令t=x-π/3,则当x->π/3时,t->0∴原式=lim(t->0){[1-2cos(t+π/3)]/sint} =lim(t->0){[1-2(cost/2-√3sint/2)]/sint} =lim(t->0)[(1-cost+√3sint)/sint] =lim(t->0)[(1-cost)/sint+√3] =√3+l...