Đáp án: 1.$\lim\sqrt{2.3^n-n+2}=+\infty$
2.$\lim\dfrac{2^{n+1}-3^n+11}{3^{n+2}+2^{n+3}-4}=-\dfrac19$
Giải thích các bước giải:
1.Ta có :
$\lim\sqrt{2.3^n-n+2}$
$=\lim \sqrt{3^n(2-\dfrac{n}{3^n}+\dfrac{2}{3^n})}$
$=\sqrt{+\infty(2-0+0)}$
$=+\infty$
2.Ta có :
$\lim\dfrac{2^{n+1}-3^n+11}{3^{n+2}+2^{n+3}-4}$
$=\lim\dfrac{2.2^{n}-3^n+11}{9.3^{n}+9.2^{n}-4}$
$=\lim\dfrac{2.(\dfrac23)^{n}-1+\dfrac{11}{3^n}}{9+9.(\dfrac23)^{n}-\dfrac4{3^n}}$
$=\dfrac{2.0-1+0}{9+9.0-0}$
$=-\dfrac19$
