求极限 lim(x趋向于0) (cosx)^(1/x^2)

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求极限lim(x趋向于0)(cosx)^(1/x^2)求极限lim(x趋向于0)(cosx)^(1/x^2)求极限lim(x趋向于0)(cosx)^(1/x^2)x->0lim(cosx)^(1/x^

求极限 lim(x趋向于0) (cosx)^(1/x^2)
求极限 lim(x趋向于0) (cosx)^(1/x^2)

求极限 lim(x趋向于0) (cosx)^(1/x^2)
x->0
lim(cosx)^(1/x^2)
=lime^(lncosx)/x^2
=e^lim(lncosx)/x^2
x->0 l hospital法则
lim (lncosx)/x^2
=lim-sinx/2xcosx
=lim -1/2cosx
=-1/2
所以原式=e^(-1/2)