Subjects calculus

Limit Absolute D768F7

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Limit Absolute D768F7


1. The problem asks to find the limit $$\lim_{x \to 3} \frac{|x - 3|}{x - 3}$$. 2. This is a classic limit involving absolute value and a linear expression. The key is to consider the behavior of the function as $x$ approaches 3 from the left and from the right. 3. Recall the definition of absolute value: $$|x - 3| = \begin{cases} x - 3 & \text{if } x \geq 3 \\ -(x - 3) & \text{if } x < 3 \end{cases}$$ 4. For $x \to 3^+$ (approaching 3 from the right), we have: $$\frac{|x - 3|}{x - 3} = \frac{x - 3}{x - 3} = 1$$ 5. For $x \to 3^-$ (approaching 3 from the left), we have: $$\frac{|x - 3|}{x - 3} = \frac{-(x - 3)}{x - 3} = -1$$ 6. Since the left-hand limit ($-1$) and right-hand limit ($1$) are not equal, the limit does not exist. 7. Therefore, the answer is "tidak ada" (does not exist). Final answer: D. tidak ada