محاسبه کنید که مقدار میانگین تابع \( g(x) = \frac{1}{x} \) در فاصله \([1, 4]\) چیست.

\( \int _{}^{}\frac{\sqrt {x}}{\sqrt [3]{x}+1} d \)

Find the volume of the solid obtained by rotating the region enclosed by \( y = 3x - x^2 \) and the x-axis for \( 0 \leq x \leq 3 \) around the x-axis using washers.

CQALCULEN LeN Limi te SuiU \( \lim _{x \rightarrow 3} \frac{3}{x-3} ; \) \( \lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3} \) \( \lim _{x \rightarrow 1} \frac{x+1}{x-1} \) \( \lim _{x \rightarrow-2} \frac{x^{2}-3 x+1}{x+2} \) \( \lim _{x \rightarrow 1} \frac{-x-2}{x^{2}-4 x+3} \)

Discur the convergene at \( [1,2] \) given that \( f(x)=x^{3}-x-1 \)

Soit \( \left(u_{n}\right) \) la sulte definie par On pose: \( V n \in \mathrm{~N} \); \( v_{n}=\frac{1}{u_{n-1}^{\prime}} \) H. Montrer que: \( (\mathrm{V} \sim \mathrm{N}): u_{n}>1 \). 2. Etudier la monotonie de la suite \( \left(u_{n}\right) \)