X Exercice 28: Calculer les limites suivantes: \( \begin{array}{ll}\text { 1. } \lim _{x \rightarrow-\infty} \ln \left(\frac{x^{2}+x+1}{3+2 x^{2}}\right) & \text { 2. } \lim _{x \rightarrow+\infty}\left(\frac{x^{3}-2}{x}\right) \\ \text { 3. } \lim _{\substack{x \rightarrow 2 \\ x<2}} \ln \left(\frac{x+1}{-x+2}\right) & \text { 4. } \lim _{\substack{x \rightarrow 0 \\ x>0}} \ln \left(\frac{\sin x}{x^{2}+1}\right)\end{array} \)

(4) show that \( \lim _{z \rightarrow a} \) \( \frac{i z^{3}+i z-1}{2 z+3 i(z-i)} \)

If \( \frac{d^{n t}}{d x^{n}}\left(e^{a x}\right)=\quad \) where \( a, b \) are constar (ii) \( a^{n-1} e^{a x} \) (iii) \( n!a^{n} \) (iii) \( (n-1)!a^{n-1} \) (iv) \( a^{n} e^{a x} \)

Calculate the volume of the solid formed by rotating the area between \( y = \sqrt{x} \) and \( y = 0 \) from \( x = 0 \) to \( x = 1 \) about the line \( y = -1 \) utilizing the washer method.

d) \( \lim _{x \rightarrow 1} \frac{\ln x}{x^{2}-1}= \)

4) Show that \( \lim _{z \rightarrow} \) \( i z^{3}+i z-1 \) \( 2 z+3 i(z-i) \)