Exercice 27: Calculer les limites suivantes : \( \begin{array}{ll}\text { 1. } \lim _{x \rightarrow 2} \ln (2-x) & \text { 2. } \lim _{x \rightarrow 1^{+}}\left(x^{2}-1\right) \ln (x-1) \\ \text { 3. } \lim _{x \rightarrow 0^{+}}\left(x^{3}-x\right) \ln x & \text { 4. } \lim _{x \rightarrow-1^{+}}\left(\frac{1}{x+1}+\ln (1+x)\right)\end{array} \)

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

Calculate the area bounded by the curves \( y = \sin(x) \) and \( y = \cos(x) \) over the interval \([0, \frac{\pi}{4}]\).

Answer any THREE. \( \lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{1}{\ln x}\right) \)

(Q6; 2,6 балла) Найдите наименьшее значение выражения \( 16 x+\frac{9}{25 x}(x>0) \), используя \( \frac{a+b}{2} \geq \sqrt{a b} \).

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) \( a^{n} e^{a x} \)