$\Large \mathrm{lim}\sqrt[4]{\dfrac{4^n+2^{n+1}}{3^n+4^{n+2}}}$ bằng:

$\Large \mathrm{lim}\sqrt[4]{\dfrac{4^n+2^{n+1}}{3^n+4^{n+2}}}$ bằng:

• A.

  0.

• B.

  $\Large \dfrac{1}{2}$.

• C.

  $\Large \dfrac{1}{4}$.

• D.

  $\Large +\infty$.

Chọn B.

Ta có: $\Large \mathrm{lim}\sqrt[4]{\dfrac{4^n+2^{n+1}}{3^n+4^{n+2}}}$ $\Large =\mathrm{lim}\sqrt[4]{\dfrac{1+2^{1-n}}{\left(\dfrac{3}{4}\right)^n+4^2}}$ $\Large =\mathrm{lim}\sqrt[4]{\dfrac{1+2.\left(\dfrac{1}{2}\right)^n}{\left(\dfrac{3}{4}\right)^n+4^2}}=\dfrac{1}{2}$

Vì $\Large \mathrm{lim}\left(\dfrac{1}{2}\right)^n=0$; $\Large \mathrm{lim}\left(\dfrac{3}{2}\right)^n=0$.