Whittaker Black

07/25/2023 · Escuela primaria

2. [Continuity] Find the values of \( a \) and \( b \) that make the following function \( f \) continuous on the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \). Justify your answer using the checklist of continuity. \[ f(x)=\left\{\begin{array}{ll}\frac{7 x^{2}}{\sqrt{x^{2}+a^{2}}-a} & \text { if } \frac{-\pi}{2}<x<0 \\ b & \text { if } x=0 \\ 3^{1-\tan (x)}+3^{1-\cot (x)} & \text { if } 0<x<\frac{\pi}{2}\end{array}\right. \]