Trong các mệnh đề sau đây mệnh đề nào là đúng?

5/20

\[\mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{\left| {{\rm{x}} - 3} \right|}}{{3{\rm{x}} - 9}} = \frac{1}{3}\].

\[\mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{\left| {{\rm{x}} - 3} \right|}}{{3{\rm{x}} - 9}} = - \frac{1}{3}\].

\[\mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{\left| {{\rm{x}} - 3} \right|}}{{3{\rm{x}} - 9}} = 0\].

Không tồn tại \[\mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{\left| {{\rm{x}} - 3} \right|}}{{3{\rm{x}} - 9}} = 0\].

Giải thích

Khi \[{\rm{x}} \to {3^ + }\]thì x > 3

Nên \[{\rm{x}} - 3 > 0 \Rightarrow \left| {{\rm{x}} - 3} \right| = {\rm{x}} - 3\]

\[\mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{\left| {{\rm{x}} - 3} \right|}}{{3{\rm{x}} - 9}} = \mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{{\rm{x}} - 3}}{{3{\rm{x}} - 9}} = \mathop {\lim }\limits_{{\rm{x}} \to {3^ + }} \frac{{{\rm{x}} - 3}}{{3.\left( {{\rm{x}} - 3} \right)}} = \frac{1}{3}\].