Câu 20: Tìm $a$ để $\lim _{x \rightarrow+\infty} \frac{a x^2+x-1}{2 x^2+1}=1$. A. $a=-2$. B. $a=0$. C. $a=1$. D. $a=2$.

`lim_[x-> +infty] [ax^2+x-1]/[2x^2+1]`

`= lim_[x->+infty] [x^2(a+1/x-1/[x^2])]/[x^2(2+1/[x^2])]`

`= lim_[x->+infty] [a+1/x-1/[x^2]]/[2+1/[x^2]]`

`= [a+0-0]/[2+0]`

`= a/2`

Mặt khác `lim_[x-> +infty] [ax^2+x-1]/[2x^2+1]=1`

`->a/2=1`

`->a=2`

`-> bbD`