1. 分母有理化,得
原式=lim(x->4) (x-4)(√(x-3)+1)/(√(x-3)-1)(√(x-3)+1)
=lim(x->4) (x-4)(√(x-3)+1)/(x-4)
=lim(x->4) (√(x-3)+1)
=1+1
=2
2 .分子分母同除以3的n+1次方,得
原式=lim(n->∞) [(-2)^n/3^(n+1)+1/3]/[(-2)^(n+1)/3^(n+1)+1]
=(0+1/3)/(0+1)
=1/3
1. 分母有理化,得
原式=lim(x->4) (x-4)(√(x-3)+1)/(√(x-3)-1)(√(x-3)+1)
=lim(x->4) (x-4)(√(x-3)+1)/(x-4)
=lim(x->4) (√(x-3)+1)
=1+1
=2
2 .分子分母同除以3的n+1次方,得
原式=lim(n->∞) [(-2)^n/3^(n+1)+1/3]/[(-2)^(n+1)/3^(n+1)+1]
=(0+1/3)/(0+1)
=1/3