lim [xtan(2/x)+(1/x^2)sinx^2] .

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lim[xtan(2/x)+(1/x^2)sinx^2].lim[xtan(2/x)+(1/x^2)sinx^2].lim[xtan(2/x)+(1/x^2)sinx^2].原式=lim[xtan(2

lim [xtan(2/x)+(1/x^2)sinx^2] .
lim [xtan(2/x)+(1/x^2)sinx^2] .

lim [xtan(2/x)+(1/x^2)sinx^2] .
原式=
lim [xtan(2/x)]+lim [(1/x^2)sinx^2]
=lim [tan(2/x)/(1/x)]+lim [(1/x^2)sinx^2]
=2+0
=2
lim (x---->+∞)1/x²=0 ,而sinx²是有界函数,所以lim [(1/x^2)sinx^2=0