Vamos calcular passo a passo usando as propriedades da função Gama: (a) \(\Gamma(6)\): Para números inteiros positivos, \(\Gamma(n) = (n-1)!\) Logo, \(\Gamma(6) = 5! = 120\). (b) \(\Gamma\left(\frac{5}{2}\right)\): Usamos a propriedade \(\Gamma\left(x+1\right) = x \Gamma(x)\). Sabemos que \(\Gamma\left(\frac{1}{2}\right) = \sqrt{\pi} \approx 1,77245\). Calculando: \[ \Gamma\left(\frac{5}{2}\right) = \left(\frac{3}{2}\right) \Gamma\left(\frac{3}{2}\right) \] E \[ \Gamma\left(\frac{3}{2}\right) = \left(\frac{1}{2}\right) \Gamma\left(\frac{1}{2}\right) = \frac{1}{2} \times 1,77245 = 0,88623 \] Então, \[ \Gamma\left(\frac{5}{2}\right) = \frac{3}{2} \times 0,88623 = 1,3293 \] (c) \(\Gamma\left(\frac{9}{2}\right)\): \[ \Gamma\left(\frac{9}{2}\right) = \left(\frac{7}{2}\right) \Gamma\left(\frac{7}{2}\right) \] \[ \Gamma\left(\frac{7}{2}\right) = \left(\frac{5}{2}\right) \Gamma\left(\frac{5}{2}\right) = \frac{5}{2} \times 1,3293 = 3,32325 \] Logo, \[ \Gamma\left(\frac{9}{2}\right) = \frac{7}{2} \times 3,32325 = 11,6317 \] Portanto, os valores são: - \(\Gamma(6) = 120\) - \(\Gamma(5/2) = 1,3293\) - \(\Gamma(9/2) = 11,6317\) A alternativa correta é a D.