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?yàn)閟in(1/x)是有界函數(shù),lim【x→0】xsin(1/x)=0求當(dāng)x趨于1時(shí)lim(x-1)sin1/x-1的極限；求當(dāng)x趨于正無(wú)窮時(shí)（（根號(hào)下x^2+1)-x)的極限求當(dāng)x趨于0時(shí)lim(1+sinx)^2/x;lim1-cos2x/(sin^2）3x的極限求當(dāng)x趨于無(wú)窮時(shí)lim(x-1)sin1/x-1的極限幫我一下，謝謝啦這題先采納，采納后向我求助，或直接提問(wèn)