Question

求这4个打勾的题的具体过程

Answer 1

(2)
lim(n->+∞) { 5^n + (-2)^n]/[ 5^(n+1) +(-2)^(n+1) ]
分子分母同时除以5^n
=lim(n->+∞) { 1 + (-2/5)^n]/[ 5 +(-2)(-2/5)^n ]
=(1+0)/(5+0)
=1/5
(2)
lim(h->0) [(x+h)^3-x^3 ]/h
=lim(h->0) (3x^2.h +3xh^2+h^3)/h
=lim(h->0) (3x^2 +3xh+h^2)
=3x^2
(6)
lim(x->+∞) (2x^3+3x+1)/(4x^5+2x+7)
分子分母同时除以 x^5
=lim(x->+∞) (2/x^2+3/x^4+1/x^5)/(4+2/x^4+7/x^5)
=(0+0+0)/(4+0+0)
=0
(8)
lim(x->1)[ 1/(1-x) -3/(1-x^3) ]
=lim(x->1){ 1/(1-x) -3/[(1-x)(1+x+x^2] }
=lim(x->1) [(1+x+x^2)-3 ] /[(1-x)(1+x+x^2)]
=lim(x->1) (x^2+x-2) /[(1-x)(1+x+x^2)]
=lim(x->1) (x+2)(x-1) /[(1-x)(1+x+x^2)]
=lim(x->1) -(x+2) /(1+x+x^2)
=-3/3
=-1