Subjects calculus

Limit X Sqrtx Abd57B

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Limit X Sqrtx Abd57B


1. The problem is to find the limit $$\lim_{x \to 0^+} \left(x - \sqrt{x}\right).\n\n2. We start by understanding the behavior of each term as $x$ approaches 0 from the right (positive side).\n- As $x \to 0^+$, $x$ approaches 0.\n- As $x \to 0^+$, $\sqrt{x}$ also approaches 0, but at a different rate.\n\n3. To evaluate the limit, we can try to simplify or analyze the expression directly:\n$$x - \sqrt{x} = \sqrt{x} \left(\sqrt{x} - 1\right).$$\n\n4. As $x \to 0^+$, $\sqrt{x} \to 0$, so $\sqrt{x} - 1 \to -1$.\nTherefore, the product approaches:\n$$0 \times (-1) = 0.$$\n\n5. Hence, the limit is:\n$$\lim_{x \to 0^+} \left(x - \sqrt{x}\right) = 0.$$