help~高数极限习题，帮助呀~

(1)原式=lim(x->0)[5sin(5x)/(5x)]
=5lim(x->0)[sin(5x)/(5x)]
=5 (利用特殊极限lim(x->0)(sinx/x)=1)
(3)原式=lim(x->0)[(sinx/cosx-sinx)/x]
=lim(x->0)[(sinx/x)(1/cosx-1)
=lim(x->0)(sinx/x)*lim(x->0)(1/cosx-1)
=1*0 (利用特殊极限lim(x->0)(sinx/x)=1)
=0
(5)原式=lim(x->0)[(1-sinx/x)/(1+sinx/x)]
=(1-1)/(1+1) (利用特殊极限lim(x->0)(sinx/x)=1)
=0
(7)原式=lim(x->0)[4(x/2)²/sin²(x/2)]
=4lim(x->0)[(x/2)/sin(x/2)]²
=4{lim(x->0)[(x/2)/sin(x/2)]}²
=4*1² (利用特殊极限lim(x->0)(sinx/x)=1)
=4
(9)原式=lim(x->0+)[x/√(2sin²(x/2))] (利用半角公式)
=lim(x->0+)[(2/√2)(x/2)/sin(x/2)]
=√2lim(x->0+)[(x/2)/sin(x/2)]
=√2*1 (利用特殊极限lim(x->0)(sinx/x)=1)
=√2

1.

lim sin5x/x=5x/x=5
sin5x用其等价无穷小5x替代

3.

lim(ta