Question

求极限：lim[√（2X+1）-3]/[√(x-2)-√2] x趋向于4?limx/[1-√(1+x)] x趋向于0 （？

Answer 1

lim[√（2X+1）-3]/[√(x-2)-√2]
分子分母同时有理化
=lim[√（2X+1）-3][√(2X+1）+3][√(x-2)+√2] / [√(x-2)-√2][√(2X+1）+3][√(x-2)+√2]
=lim[2X+1-9][√(x-2)+√2] / [x-2-2][√(2X+1）+3]
=lim 2[X-4][√(x-2)+√2] / [x-4][√(2X+1）+3]
=lim 2[√(x-2)+√2] / [√(2X+1）+3]
=4√2/6
=2√2/3
lim x/[1-√(1+x)]
=lim x[1+√(1+x)] / [1-√(1+x)][1+√(1+x)]
=lim x[1+√(1+x)] / [1-1-x]
=lim x[1+√(1+x)] / [-x]
=lim -[1+√(1+x)]
=-2
(-1)^0.1无意义,一般指数如果不是整数,通常不用负数做底数.,7,求极限：lim[√（2X+1）-3]/[√(x-2)-√2] x趋向于4?limx/[1-√(1+x)] x趋向于0 （-1）^0.1=?