Find the equations of the tangent and normal lines to the curve \( y=\sqrt[3]{5-x} \) at the point \( (-3,2) \). Show that the tangents to the curve \( y=\frac{1}{6}\left[3 x^{5}+2 x^{3}-3 x\right] \) at the points \( x= \pm 3 \) are parallel. W

3)- Pour tout \( n \in \mathbb{N}^{*} \), On pose : \( S_{n}=\sum_{k=n+1}^{2 n} \frac{g^{-1}\left(u_{k}\right)}{k} \) a) - Montrer que : \( \left(\forall n \in \mathbb{N}^{*}\right), g^{-1}\left(u_{n+1}\right) \cdot \sum_{k=n+1}^{2 n} \frac{1}{k} \leq S_{n} \leq g^{-1}\left(u_{2 n}\right) \cdot \sum_{k=n+1}^{2 n} \frac{1}{k} \) b)- Déduire la limite de la suite \( \left(S_{n}\right)_{n \in \mathbb{N}^{*}} \) \( \quad\left(\right. \) On admet que \( \left.\lim _{n \rightarrow+\infty} \sum_{k=n+1}^{2 n} \frac{1}{k}=\ln 2\right) \)

Find the derivative of \( \begin{array}{l}y=4 e^{\sin x} \\ y=2 x^{5} \cos x\end{array} \)

Find the arclength of \( y=4 x-5 \) on \( 0 \leq x \leq 3 \)

Find the arclength of \( y=2 x^{2}+1 \) on \( 0 \leq x \leq 1 \) Question Help: Video

Find the arclength of \( y=2 x^{2}+1 \) on \( 0 \leq x \leq 1 \)