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  1. Limit of a square-root difference ●●○○○ 20 ptsFind lim⁡n→∞n(n+1−n)\lim_{n\to\infty} \sqrt{n}\left(\sqrt{n+1}-\sqrt{n}\right). Give your answer as a decimal.
  2. Parameters of a square-root limit ●●●○○ 50 ptsFind the values of the constants aa and bb such that lim⁡x→1a−x−b+xx−1=−12\lim_{x \to 1} \frac{\sqrt{a-x} - \sqrt{b+x}}{x-1} = -\frac{1}{2}.
  3. Limit at root 6 with radicals ●●●○○ 50 ptsFind lim⁡x→65+2x−(3+2)x2−6\lim_{x\to\sqrt{6}}\frac{\sqrt{5+2x}-(\sqrt{3}+\sqrt{2})}{x^2-6}. Round to two decimal places.