Tìm giới hạn vô cực sau: lim(1.001)^n lim((-2)-4.3^n+1) lim √2.3^n-4^n

$\lim \:\left(1\cdot \:\:001\right)^n$

$=\lim _{x\to \infty \:}\left(1\right)$

$=1$

____________________

$\lim \left(-2-4.3^x+1\right)$

$=-\lim \:2-\lim \:4\:.\:3^x+\lim \:1$

$=-2-\infty \:+1$

$=-\infty \:$

____________________

$\lim \:\sqrt{2}.3^n-4^n$

$=\lim \:\left(3^x\sqrt{2}\left(1-\dfrac{4^x}{\sqrt{2}.\:\:3^x}\right)\right)$

$=\sqrt{2}.\:\lim \:\:\left(3^x\left(1-\dfrac{4^x}{\sqrt{2}.\:\:3^x}\right)\right)$

$=\sqrt{2}.\:\lim \:\left(3^x\right).\:\lim \:\:\left(1-\dfrac{4^x}{\sqrt{2}.\:3^x}\right)$

$=\sqrt{2}\cdot \infty \cdot \left(-\infty \:\right)$

$=-\infty \:$