求高手教我做第3 9 15 这三道数学极限题！！小弟感激不尽！！

Answer 1

这三个极限全部满足罗必塔法则的应用前提，所以有：

lim[tan(2x)/tan(5x)]

=lim[(sec2x)^2 * 2]/[(sec5x)^2*5]

=lim[1^2 * 2]/[1^2 * 5]

=2/5

lim(1-cos2x)/(xsin2x)

=lim2(sinx)^2/(2xsinxcosx)

=lim(sinx)/(xcosx)

=lim(cosx)/(cosx-xsinx)

=lim1/(1-0*0)

=1

limx[ln(x+1)-lnx]

=lim[ln(x+1)-lnx]/(1/x)

=lim[1/(x+1)-1/x)]/(-1/x^2)

=limx^2/[x(x+1)]

=lim1/[1+1/x]

=lim1/[1+0]

=1

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小弟不胜感激！！