Question

两道高中数学题求极限

两道高中数学题求极限第18和20题，最好有过程，谢谢！

Answer 1

18.
lim [¾- (x+1)/x²]/(x-2)
x→2
=lim [3x²-4(x+1)]/[4x²(x-2)]
x→2
=lim (3x²-4x-4)/[4x²(x-2)]
x→2
=lim (x-2)(3x+2)/[4x²(x-2)]
x→2
=lim (3x+2)/(4x²)
x→2
=(3·2+2)/(4·2²)
=½
20.
lim [(x-1)³-1]/(x-2)
x→2
=lim [(x-1)-1][(x-1)²+(x-1)+1]/(x-2)
x→2
=lim (x-2)(x²-x+1)/(x-2)
x→2
=lim (x²-x+1)
x→2
=2²-2+1
=3