极限求详解!（1）limx→0(tan2x)/(6x)（2）limx→1sin(x-1)/(√x-1)(3)limx→∞[（2x^2+1)/(x+2)]*sin2/x

Question

极限求详解!
（1）limx→0(tan2x)/(6x) （2）limx→1sin(x-1)/(√x-1) (3)limx→∞[（2x^2+1)/(x+2)]*sin2/x

Answer 1

1）
limx→0(tan2x)/(6x)
=limx→0(2x)/(6x)
=1/3
（2）limx→1sin(x-1)/(√x-1)
=limx→1(x-1)/(√x-1)
=limx→1(√x+1)
=2
3) limx→∞[（2x^2+1)/(x+2)]*sin2/x
=limx→∞[（2+1/x^2)/(1+2/x)]*limx→∞(x*sin2/x)
=2*2
=4