求下列函数的极限的方法

1. lim xsin(1/x)
x→∞

=lim sin(1/x)/(1/x)=1
x→∞

2. lim[1/(x-2)]^(1/x-3)
x→3
=lim {[1+(3-x)/(x-2)]^(x-2)/(3-x)}^1/(x-2)=1/e
x→3

3. lim (x^2)[(cos(2/x)-1]
x→∞
=lim{-2[sin(1/x)]^2}/(1/x^2)
x→∞
=(-2)[limsin(1/x)/(1/x)]^2
x→∞
=-2

1.sin(1/x)/1/x=1
2.[1+(3-x)/(x+2)]^(x+2)/(3-x)*(3-x)/(x+2)*(1/(x-3))
=e^(-1/5)
3.x趋于无穷，1/x趋于0，cos(2/x)-1~~~-(1/x)^2
原式=-1