Question Exercise 1: Limits 3) Write the reference limits of the function $\ln x$ 4) Using these limits, calculate the limits of the following functions at the bounds of their domain: a) $f(x)=x^{2}-2+\ln x$ b) $g(x)=x^{2}+(2-\ln x)^{2}$ c) $h(x)=\frac{\ln (x+2)}{1+x^{2}}$ d) $l(x)=x(\ln x)^{2}$
Exercise 2: Derivative and sign study of the derivative Calculate the derivative function of the following functions and study the sign of the derivative: 4) $f(x)=-1+(\ln x)^{2}$ 5) $g(x)=\ln \frac{x}{x+1}$ 6) $h(x)=\ln \left|\frac{x-2}{x+4}\right|$
Exercise 3: Complex numbers 3) Solve the equation $z^{2}-2 i z-2=0$ in the set $\mathbb{C}$ of complex numbers 4) Let $z_{1}$ and $z_{2}$ be the solutions of this equation such that $\operatorname{Re}\left(z_{1}\right)>\operatorname{Re}\left(z_{2}\right)$.