Question

这几道数学题怎么做？

Answer 1

第1题为常规求极限题目，第2、4题需对求极限的函数进行化简，第5题需应用到求极限的定理2，大家只要多练习，就可以熟能生巧啦

Answer 2

(1)

lim(x->2) (x^2+5)/(x^2-3)

=(4+5)/(4-3)

=9

(2)

lim(x->1) (x^2-2x+1)/(x^2-x)

=lim(x->1) (x-1)^2/[x(x-1)]

=lim(x->1) (x-1)/x

=0

(3)

lim(x->+∞) (1-x-x^3)/(x+x^3)

分子分母同时除x^3

=lim(x->+∞) (1/x^3-1/x^2-1)/(1/x^2+1)

=(0-0-1)/(0+1)

=-1

(4)

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)

=-(1+2)/(1+1+1)

=-1

(5)

|sinx|≤1 and  lim(x->+∞) 1/x=0

=>

lim(x->+∞) sinx/x =0

Answer 3

解答如下

Answer 4

1.直接代，得9.
2.约去x-1,答：0.
3.最高次项系数之比，得-1.

4.1/(1-x)-3/(1-x^3)

=(1+x+x^2-3)/[(1-x)(1+x+x^2)]
=-(x+2)/(1+x+x^2)-->-1.
5.1
可以吗？

Answer 5