57. Pour chaque suite, indiquer si elle est arithmé- tique (en précisant sa raison) ou non. \( \begin{array}{ll}\text { 1. } u_{n}=4 n+3 & \text { 2. } v_{n}=n^{2}-3\end{array} \) \( \begin{array}{ll}\text { 3. } w_{n}=5-3 n & \text { 4. }\left\{\begin{array}{l}t_{0}=2 \\ t_{n+1}=t_{n}+7\end{array}\right. \\ \text { 5. }\left\{\begin{array}{ll}z_{0}=-2 & \text { 6. } k_{n}=(2 n+3)^{2}-4 n^{2} \\ z_{n+1}=z_{n}+n & \end{array}\right.\end{array} \)

7. Исследуйте но чётность и нечетность функции а) \( \mathrm{y}=4 \mathrm{x}-2 \mathrm{x}^{3}+6 \mathrm{x}^{5} \quad \); б) \( f(x)=\frac{5}{x^{4}+4 x^{2}} \)

b) \( \left(\frac{6}{4} \sqrt{48}+\sqrt{75}-\frac{1}{2} \sqrt{12}\right)+\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{27}} \)

20. Vereinfache im Kopf. \( \begin{array}{lll}\text { a) }\left(5^{\frac{4}{5}}\right)^{\frac{5}{2}} & \text { b) }\left(36^{\frac{3}{4}}\right)^{\frac{2}{3}} & \text { c) }\left(49^{-\frac{6}{7}}\right)^{\frac{7}{12}}\end{array} \)

Find \( \|\mathbf{v}\| \). \( \mathbf{v}=-3 \mathbf{i}+7 \mathbf{j} \) \( \begin{array}{l}\|\mathbf{v}\|=\square \\ \text { (Simplify your answer. Type an exact answer, using radicals as needed.) }\end{array} \)

2. \( \frac{1}{\sqrt{3}+\sqrt{2}} \div \frac{1}{\sqrt{4}+\sqrt{3}} \div \frac{1}{\sqrt{5}+\sqrt{4}}= \) ?