Pregunta: 2. En qué puntos la finción f(z)={x2−1z4−13/2z=±2z=±1 in continu? IUSTIFIQUE BIEN SU RESPUESTA (1.5 PUNTOS.)

Clearly given function is continuous for all z $\ne \pm 1$

now we see that f is continuous or not at $\mathrm{z}\pm 1$

now $\underset{\mathrm{z}\to -1}{lim}\mathrm{f}\left(\mathrm{z}\right)=\underset{\mathrm{z}\to -1}{lim}\frac{{\mathrm{z}}^4-1}{{\mathrm{z}}^2-1}=\underset{\mathrm{z}\to -1}{lim}\frac{({\mathrm{z}}^2-1)({\mathrm{z}}^2+1)}{{\mathrm{z}}^2-1}=\underset{\mathrm{z}\to -1}{lim}({\mathrm{z}}^2+1)={(-1)}^2+1=2$