Differences of square roots

Limit of a sum with a cube root ●○○○○ 10 ptsCompute $\lim_{x \to 10} \left(4x + \sqrt[3]{x - 2}\right)$ .
Limit of a square-root difference ●●○○○ 20 ptsFind $\lim_{n\to\infty} \sqrt{n}\left(\sqrt{n+1}-\sqrt{n}\right)$ . Give your answer as a decimal.
Limit of nested square roots ●●○○○ 20 ptsFind $\lim_{x\to\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right)$ .
Limit of quotient of root differences ●●○○○ 20 ptsFind $\lim_{x \to 0} \frac{(1+x)^{1/2} -1}{(1+x)^{1/3} -1}$ without using L'Hôpital's rule. Round to three decimal places.
Parameters of a square-root limit ●●●○○ 50 ptsFind the values of the constants $a$ and $b$ such that $\lim_{x \to 1} \frac{\sqrt{a-x} - \sqrt{b+x}}{x-1} = -\frac{1}{2}$ .
Limit of a ratio with roots ●●●○○ 50 ptsFind $\lim_{x\rightarrow 2}\frac{2-\sqrt{2+x}}{2^{\frac{1}{3}}-(4-x)^{\frac{1}{3}}}$ without using L'Hospital's rule. Round your answer to two decimal places.
Limit at root 6 with radicals ●●●○○ 50 ptsFind $\lim_{x\to\sqrt{6}}\frac{\sqrt{5+2x}-(\sqrt{3}+\sqrt{2})}{x^2-6}$ . Round to two decimal places.

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