lim(sinx-sin1)/x-1 x趋近于1 lim(根号2-根号下(1+cosx)/sin2x

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lim(sinx-sin1)/x-1 x趋近于1 lim(根号2-根号下(1+cosx)/sin2x

lim(sinx-sin1)/x-1 x趋近于1 lim(根号2-根号下(1+cosx)/sin2x
lim(sinx-sin1)/x-1 x趋近于1 lim(根号2-根号下(1+cosx)/sin
2x

lim(sinx-sin1)/x-1 x趋近于1 lim(根号2-根号下(1+cosx)/sin2x
1,o/o型,用洛必达法则
原式=lim(x→1) cosx/1
=cos1
2,∵√(1+cosx)=√{2[cos(x/2)]^2}=√2*cos(x/2)
∴√2-√(1+cosx)=√2*[1-cos(x/2)]
等价无穷小:当x→0时,cosx=1-1/2*x^2,sinx=2x
∴原式=lim(x→0) √2*[1-cos(x/2)]/sin2x
=lim(x→0) √2*1/2*(1/2*x)^2/2x
=lim(x→0) √2/16*x
=0