Calculate the area enclosed between the lines \( y = 2x + 3 \) and \( y = x^2 \).

a) \( D[(1-x) \sqrt{1+x}] \)

Let \( y-x e^{y}=1 \), then \( d y(0)= \)

(vi) \( \mathrm{L}^{-1}\left\{\tan ^{-1} \frac{1}{\mathrm{p}}\right\}= \)

3. (a) Montrer que pour tout réel \( t \geq 0: t-\frac{t^{3}}{3} \leq \arctan (t) \leq t \) (b) Calculer la limite : \( \lim _{x \rightarrow+\infty} x\left(1-x \arctan \left(\frac{1}{x}\right)\right) \).

4. (15б) Выясните, является ли функция \( z=\ln \left(x^{2}+y^{2}+2 y+1\right) \) решением уравнения \( \frac{\partial^{2} z}{\partial x^{2}}+\frac{\partial^{2} z}{\partial y^{2}}=0 \)