32;(4)lim
x→03x2+2x
3224x 2x+x4x 2x+1=1.解lim=limx→03x2+2xx→03x+22
(x+h)2 x2(5)lim;h→0h
222(x+h)2 x2解lim=lim=lim(2x+h)=2x.h→0h→0h→0hh(6)lim(2 1+12;x→∞xx
解lim(2 1+1=2 lim1+lim1=2.
x→∞x→∞x→∞xx
(7)lim
x2 1;x→∞2x2 x 1
2
1 12
x 1=lim=1.解lim
x→∞2x x 1x→∞
2 2xx
2;(8)lim42
x→∞x 3x 1
2
x=0(分子次数低于分母次数,极限为零).解limx+x→∞x 3x 1
1+1
2x=lim23=0.或lim4x+2
x→∞x 3x 1x→∞
1 2 1xx
2
(9)limx 6x+8;x→4x 5x+4
2(x 2)(x 4)x解lim 6x+8=lim=limx 2=4 2=2.x→4x 5x+4x→4(x 1)(x 4)x→4x 14 13
(10)lim(1+12 12;
x→∞x
解lim(1+1)(2 12=lim(1+1 lim(2 12=1×2=2.
x→∞x→∞xxx→∞xx(11)lim(1+1+1+ +1);
n→∞2