A calculus problem by Abdulrahman El Shafei

Calculus Level 3

$\large \lim_{ x\to{ 3 }^{ + } }\dfrac { 3-x }{ \left| 3-x \right| } =\, ?$

Notation: $| \cdot |$ denotes the absolute value function .

1 -1

1 solution

Michael Huang
Dec 2, 2016

At $x \geq 3$ , $|3 - x| = -(3 - x)$ . Thus, $\lim_{x\rightarrow 3^{+}} \dfrac{3 - x}{|3 - x|} = \lim_{x\rightarrow 3} \dfrac{(3 - x)}{-(3 - x)} = \boxed{-1}$

A calculus problem by Abdulrahman El Shafei

1 solution

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