Search problems

4 problems match “rationalising denominators”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Limit of nested square roots ●●○○○ 20 ptsFind $\lim_{x\to\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right)$.
2. 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.
3. Sum of conjugate fractions ●●○○○ 20 ptsSimplify $\frac{3+\sqrt{5}}{3-\sqrt{5}}+\frac{3-\sqrt{5}}{3+\sqrt{5}}$.
4. 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.