![](https://iknow-base.cdn.bcebos.com/lxb/notice.png)
求大佬帮忙解决一下这几道题
(11)
lim(x->0) (x-sinx)/ (2x^3 +x^2)
=lim(x->0) (1/6)x^3/ (2x^3 +x^2)
=0
抄写题目时可能出错!
估计应该
lim(x->0) (x-sinx)/ (2x^3 +x^4)
=lim(x->0) (1/6)x^3/ (2x^3 +x^4)
=1/12
ans : C
(12)
x->无穷
2^(1/x) =1 +(ln2)(1/x) + o(1/x)
3^(1/x) =1 +(ln3)(1/x) + o(1/x)
[ 2^(1/x) +3^(1/x)]/2 = 1 +(1/2)(ln6)(1/x) + o(1/x)
lim(x->无穷) { [ 2^(1/x) +3^(1/x)]/2 }^x
=lim(x->无穷) [ 1 +(1/2)(ln6)(1/x) ]^x
=e^[(1/2)(ln6)]
=√6
ans :B
(13)
f(x)
=arcsinx/x ; 0<x<1
=a-1 ; x=0
=xsin(1/x) +b ; x<0
f(0+) =lim(x->0) arcsinx/x =1
f(0-) =lim(x->0-) [xsin(1/x) +b ] =b
f(0) =a-1
f(0)=f(0-)=f(0+)
1=b=a-1
a=2, b=1
ans: A
(14)
lim(h->0) [f(a)-f(a-2h) ]/h
=2lim(h->0) [f(a)-f(a-2h) ]/(2h)
=2f'(a)
ans: C