求极限lim(sin(w符号)x)/x(x→0)
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求极限lim(sin(w符号)x)/x(x→0)
求极限lim(sin(w符号)x)/x(x→0)
求极限lim(sin(w符号)x)/x(x→0)
0/0型极限,应用洛必达法则
lim(sin(wx))/x
=lim wcos(wx)/1
当x趋向0时
=wcos(w×0)/1
=w
0/0型,可以用洛必达法则
lim(x→0)(sinwx)/x
上下同时求导
=lim(x→0)wcoswx/1
x→0,coswx→1
所以极限=w
wxcosx-xsinwx/2x
利用等价无穷小,sinωx ∽ ωx ,当x-->0时
则可知 lim(sin(ωx))/x (x->0)=limωx/x (x->0)
=ω
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