<h2> For §§N0§§ </h2> <p>(a) Berechne: \( \sqrt{§§V1(4,25,3)§§} \times \sqrt{§§V2(2,15,2)§§} \)</p> <p>(b) Vereinfache den Ausdruck: \( \frac{\sqrt{§§V3(9,36,3)§§}}{\sqrt{§§V4(2,10,2)§§}} + \int_{-\infty}^{\infty} e^{-\frac{x^2}{2}} \left(1 + \frac{1}{2} \sin^2(3x) + \frac{\alpha}{\beta}\sqrt{\gamma+\delta} \cdot \frac{\sqrt[3]{\theta^2 + \phi^2}}{\psi + \frac{\omega}{\chi}}\right) \,dx \)</p> <p>(c) Multipliziere: \( (\sqrt{§§V5(3,20,2)§§} + \sqrt{§§V6(2,12,2)§§}) \times (\sqrt{§§V7(4,18,2)§§} - \sqrt{§§V8(1,9,1)§§}) \)</p> <p>(d) Dividiere: \( \frac{\sqrt{§§V9(16,64,8)§§}}{\sqrt{§§V10(4,16,2)§§}} \)</p> <p>(e) Vereinfache den Ausdruck: \( \begin{equation} x = a_0 + \frac{1}{\displaystyle a_1 + \frac{1}{\displaystyle a_2 + \frac{1}{\displaystyle a_3 + a_4}}} \end{equation} \)</p> <p>(f) Berechne: \( \frac{\sqrt{§§V13(25,100,5)§§} \times \sqrt{§§V14(49,196,7)§§}}{\sqrt{§§V15(9,36,3)§§}} \)</p> <p>(g) Multipliziere und vereinfache: \( (\sqrt{§§V16(5,25,5)§§} + \sqrt{§§V17(3,15,3)§§})^2 \)</p> <p>(h) Dividiere: \( \frac{\sqrt{§§V18(81,324,9)§§}}{\sqrt{§§V19(9,36,3)§§}} - \begin{bmatrix} \int_{0}^{1} e^{2t}\sin(t)\,dt & \frac{\cos^2(3\theta)}{\sqrt{2}} & 0 & \frac{\pi}{4} & \ln(2) \\ \frac{\sqrt{5}}{\phi} & \int_{-\infty}^{\infty} \frac{\sin^2(x)}{x^2}\,dx & \frac{1}{\sqrt[3]{\alpha + \beta}} & \frac{\gamma^2}{\delta} & \frac{\sqrt{\pi}}{2} \\ \frac{\theta}{2\pi} & \frac{1}{\sqrt{3}} & \int_{0}^{1} \frac{e^{2t}}{\sqrt{t}}\,dt & \frac{\omega}{\chi} & \frac{\sqrt{2}}{\sqrt{\pi}} \\ \ln(\sqrt{\pi}) & \frac{\sqrt[4]{\pi^3}}{\sqrt{\alpha}} & \frac{\sqrt{\beta}}{\sqrt[3]{\gamma}} & \int_{-\pi}^{\pi} \cos^2(\phi)\,d\phi & \frac{\sqrt[5]{\delta}}{\sqrt[6]{\varepsilon}} \end{bmatrix} \)</p> <p>(i) Berechne: \( \sqrt{§§V20(20,100,10)§§} \div \sqrt{§§V21(2,8,2)§§} \)</p> <p>(j) \( \mathcal{L}_{\mathcal{T}}(\vec{\lambda}) = \sum_{\mathbf{x},\mathbf{s}\in\mathcal{T}} \log P(\mathbf{x}|\mathbf{S}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2} \) </p>