x趋近于0,lim(1-根号下cosx)/x(1-cos根号下x)

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x趋近于0,lim(1-根号下cosx)/x(1-cos根号下x)

x趋近于0,lim(1-根号下cosx)/x(1-cos根号下x)
x趋近于0,lim(1-根号下cosx)/x(1-cos根号下x)

x趋近于0,lim(1-根号下cosx)/x(1-cos根号下x)
=lim (1-cosx)/[x(1-cos根号下x)·(1+根号下cosx)]
=(1/2)·lim (x²/2)/[x(1-cos根号下x)]
=(1/4)·lim x/(1-cos根号下x)
=(1/4)·lim x/((根号下x)²/2)
=1/2