What does the Fundamental Theorem of Calculus state about the relationship between differentiation and integration?

أوجد قيمة النهاية \( \lim _{x \rightarrow \infty} \frac{3 x^{2}-x+1}{2 x^{3}+4}= \)

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 arclength of \( y=4 x^{3 / 2} \) on \( 2 \leq x \leq 4 \)

\( \int ( \pi x ^ { 3 + 1 } ) ^ { 4 } 3 \pi x ^ { 2 } d \)

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