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3 problems match “nested radicals”. Clear

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1. Limit of nested square roots ●●○○○ 20 ptsFind $\lim_{x\to\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right)$.
2. Radical equation with cube roots ●●●○○ 50 ptsSolve the equation $\sqrt[3]{9-\sqrt{x+1}}+\sqrt[3]{7+\sqrt{x+1}}=4$.
3. 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.