求当x趋于0时lim (1+x)^1/2-(1+x)^1/3/x;lim(xsin(1/x)+(1/x)sinx0的极限

lim【x→0】[(1+x)^1/2-(1+x)^1/3]/x
=lim【x→0】{1+x/2+o(x)-[1+x/3+o(x)]}/x
=lim【x→】(x/6)/x
=1/6
lim【x→0】[xsin(1/x)+(1/x)sinx]
=lim【x→0】xsin(1/x)+lim【x→0】(1/x)sinx
=0+lim【x→0】(sinx)/x
=1
因为sin(1/x)是有界函数,lim【x→0】xsin(1/x)=0求当x趋于1时lim(x-1)sin1/x-1的极限；求当x趋于正无穷时（（根号下x^2+1)-x)的极限求当x趋于0时lim(1+sinx)^2/x;lim1-cos2x/(sin^2）3x的极限求当x趋于无穷时lim(x-1)sin1/x-1的极限帮我一下，谢谢啦这题先采纳，采纳后向我求助，或直接提问