Câu 1: $g(x)= \dfrac{e^{2x}}{e^{2x} +1}$
$a)\quad \lim\limits_{x\to \infty}g(x)$
$= \lim\limits_{x\to \infty}\dfrac{e^{2x}}{e^{2x} +1}$
$= \lim\limits_{x\to \infty}\dfrac{1}{1 + \dfrac{1}{e^{2x}}}$
$= \dfrac{1}{1 +0}$
$= 1$
$b)\quad \displaystyle\int g(x)dx$
$= \displaystyle\int\dfrac{e^{2x}}{e^{2x} +1}dx$
$= \dfrac12\displaystyle\int\dfrac{d\left(e^{2x}+1\right)}{e^{2x} +1}$
$= \dfrac12\ln\left(e^{2x}+1\right) + C$
Câu 2:
$\quad 10dx - x(x^{10} +1)^2dy = 0$
$\Leftrightarrow dy = \dfrac{10}{x(x^{10} +1)^2}dx$
$\Leftrightarrow y = \displaystyle\int\dfrac{10}{x(x^{10} +1)^2}dx$
$\Leftrightarrow y = \dfrac{1}{x^{10} + 1} - \ln\left(x^{10} +1\right) + 10\ln x + C$
