Find the value of the limit $\lim _ { x \rightarrow 2 ^ { - } } \frac { | x - 2 | } { x - 2 }$
A)1
B)-2
C) $\frac { 1 } { 2 }$
D)-4
E)-1
F)4
G)
$- \frac { 1 } { 2 }$
H)2

Question

Find the value of the limit $\lim _ { x \rightarrow 2 ^ { - } } \frac { | x - 2 | } { x - 2 }$
A)1
B)-2
C) $\frac { 1 } { 2 }$
D)-4
E)-1
F)4
G)
$- \frac { 1 } { 2 }$ 
H)2

Quizplus · Accepted Answer

When $x$ approaches $2$ from the left ($x \rightarrow 2^-$), $x - 2 < 0$, so $|x - 2| = -(x - 2)$. Thus, the expression simplifies to $\frac{-(x - 2)}{x - 2} = -1$.

Find the Value of the Limit lim⁡x→2−∣x−2∣x−2\lim _ { x \rightarrow 2 ^ { - } } \frac { | x - 2 | } { x - 2 }limx→2−​x−2∣x−2∣​

Find the Value of the Limit $\lim _ { x \rightarrow 2 ^ { - } } \frac { | x - 2 | } { x - 2 }$