The answer should be ✓3/6

Question

The answer should be ✓3/6

Asked on March 28, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-28T22:59:32.719Z

❌ Incorrect. Your proposed answer $\frac{\sqrt{3}}{6}$ is incorrect. After simplifying the numerator, we had $2x$, not $x$. $$ \lim_{x \to 0} \frac{2x}{x(\sqrt{2x+3} + \sqrt{3})} $$ Canceling $x$ gives: $$ \lim_{x \to 0} \frac{2}{\sqrt{2x+3} + \sqrt{3}} $$ Substituting $x=0$: $$ \frac{2}{\sqrt{2(0)+3} + \sqrt{3}} = \frac{2}{\sqrt{3} + \sqrt{3}} = \frac{2}{2\sqrt{3}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} $$

Accepted Answer · 2026-03-28T22:59:32.719Z

❌ Incorrect. Your proposed answer $\frac{\sqrt{3}}{6}$ is incorrect. After simplifying the numerator, we had $2x$, not $x$. $$ \lim_{x \to 0} \frac{2x}{x(\sqrt{2x+3} + \sqrt{3})} $$ Canceling $x$ gives: $$ \lim_{x \to 0} \frac{2}{\sqrt{2x+3} + \sqrt{3}} $$ Substituting $x=0$: $$ \frac{2}{\sqrt{2(0)+3} + \sqrt{3}} = \frac{2}{\sqrt{3} + \sqrt{3}} = \frac{2}{2\sqrt{3}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} $$