计算下列极限：
(1)limx→2(54+3x2+2)；(2)limx→1[(4x2+x+x)/(x+1)]；
(3)limx→∞(1-1/x+1/x2)；(4)limx→∞(2x2+1)/(1-3x2)；
(5)limx→0(e
计算下列极限：
(1)limx→2(54+3x2+2)；(2)limx→1[(4x2+x+x)/(x+1)]；
(3)limx→∞(1-1/x+1/x2)；(4)limx→∞(2x2+1)/(1-3x2)；
(5)limx→0(ex+sinx+x2)；(6)limx→∞[(x2+1)/(x4+3x-1)]；
(7)limx→∞[x2/(1-x2)+x2/(1+x)]；(8)limx→3[(√1+x-2)/(x-3)]
【正确答案】：(1)limx→2(5x4+3x2+2)=5•24+3•22+2=94 (2)limx→1[(4x2+x+1)/(x+1)]=(4•12+1+1)/(1+1)=3 (3)limx→∞(1-1/x+1/x2)=1-0+0=1 (4)limx→∞[(2x2+1)/(1-3x2)]=limx→∞[(2+1/x2)/(1/x2-3)]=[limx→∞(2+1/x2)]/[limx→∞(1/x2-3)=-(2/3) (5)limx→0(ex+sinx+x2)=limx→0ex+limx→0sinx+limx→0x2=1 (6)limx→∞[(x2+1)/(x4+3x-1)]=limx→∞[(1/x2+1/x4)/(1+3/x3-1/x4)]=[limn→∞(1/x2+1/x4)]/[limn→∞(1+3/x3-1/x4)=0 (7)limx→∞[x2/(1-x2)+x2/(1+x)]=lim[x2/(1-x2)]=limx→∞[1/(x1/2-1)]=-1 (8)limx→3[(√1+x-2)/(x-3)]=limx→3[(√1+x-2)(√1+x+2)]/[(x-3)(√1+x+2)]， =limx→3[1/(√1+x+2)]=1/4
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