Use Newton's method to find an approximate solution to \( x^{2}-2=0 \), starting from an initia estimate \( x_{1}=2 \). Iterate until 6 iterations. Hints: \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=2 \boldsymbol{x} \) Marks)

\( 2 = \int \frac { x ^ { 2 } d x } { 4 x ^ { 2 } + 1 } = \)

HALLAR DERIVADA DE \( h(x) \) USANDO LAREGLA DE CA CADENA: \( h(x)=e^{5-x}+\ln ^{5}(x) \)

2) \( \lim _{x \rightarrow 0}\left(\frac{1}{x \sqrt{1+x}}-\frac{1}{x}\right)= \)

Ejercicio 3. Calcular \[ \begin{array}{ll}\text { i) } \int_{1}^{2}(4 x-2) e^{3 x+1} \mathrm{~d} x & \text { ii) } \int \frac{\cos (x)}{\operatorname{sen}(x)-\operatorname{sen}^{3}(x)} \mathrm{d} x\end{array} \quad \text { iii) } \int_{2}^{e} \frac{\sqrt{\ln (x)+2}}{x} \mathrm{~d} x \]

Знайти площу фігури, обмеж а) \( y=4 x-x^{2} ; \)