在下列极限中，其值等于2的是（）A．limx→1x2−6x+13x2−1B．limx→∞2x2+2x3+2C．limx→−1(3x+6x3+1−1x+1)D．limn→∞C0n+C1n+…+Cnn1+2+22+…+2n

Question

在下列极限中，其值等于2的是（　　）

A．

lim

x→1

(x2−6x+1)/(3x2−1)
B．

lim

x→∞

(2x2+2)/(x3+2)
C．

lim

x→−1

((3x+6)/(x3+1)−(1)/(x+1))
D．

lim

n→∞

(C0n+C1n+…+Cnn)/(1+2+22+…+2n)

Answer 1

由于

lim

x→1

(x2−6x+1)/(3x2− 1)=(12−6×1+1)/(3×12−1)=-2
     

lim

x→∞

(2x2+2)/(x3+2)＝

lim

x→∞

((2x2+2)/(x3))/(1+(2)/(x3))＝0
    

lim

x→−1

((3x+6)/(x3+1)−(1)/(x+1))＝

lim

x→−1

(5−x)/(x2−x+1)=2
    

lim

n→∞

(Cn0+Cn1+…+ Cnn)/(1+2+22+…+2n)=

lim

n→∞

(2n)/((1−2n+1)/(1−2))=

lim

n→∞

(1)/(2−(1)/(2n))=(1)/(2)
故选C