Question

极限求详解!（1）limx→0(tan2x)/(6x) （2）limx→1sin(x-1)/(√x-1) (3)limx

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