Tìm tịm cận y=2x-1/x-1

Đáp án: $\left\{ \begin{array}{l}
TCN:y = 2\\
TCD:x = 1
\end{array} \right.$

Giải thích các bước giải:

$\begin{array}{l}
y = \dfrac{{2x - 1}}{{x - 1}}\\
Dkxd:x - 1\# 0 \Leftrightarrow x\# 1\\
\mathop {\lim }\limits_{x \to \infty } y = \mathop {\lim }\limits_{x \to \infty } \dfrac{{2x - 1}}{{x - 1}} = 2\\
 \Leftrightarrow \left\{ \begin{array}{l}
TCN:y = 2\\
TCD:x = 1
\end{array} \right.
\end{array}$

$\lim\limits_{x\to 1^+}y=\lim\limits_{x\to 1^+}\dfrac{2x-1}{x-1}=+\infty$

$\to$ TCĐ: $x=1$

$\lim\limits_{x\to \pm\infty}y=\lim\limits_{x\to \infty}\dfrac{ 2-\dfrac{1}{x}}{1-\dfrac{1}{x}}=2$

$\to$ TCN: $y=2$