What's 2.5! ?
A 3.32038
B 3.32335
What's 0 ÷ 0 ?
A ∞
B indefinite
What's 00 ?
A 1
B indefinite
+26367 What's 2.5! ?
\(\begin{array}{rcll} 2.5! &=& \Gamma(3.5) \\ &=& \Gamma(2.5+1) \\ &=& 2.5\cdot\Gamma(2.5) \\ &=& 2.5\cdot\Gamma(1.5+1) \\ &=& 2.5\cdot 1.5\cdot\Gamma(1.5) \\ &=& 2.5\cdot 1.5\cdot\Gamma(0.5+1) \\ &=& 2.5\cdot 1.5\cdot 0.5\cdot\Gamma(0.5) \qquad \Gamma(0.5) = \sqrt{\pi}\\ &=& 2.5\cdot 1.5\cdot 0.5\cdot\sqrt{\pi}\\\\ &=& 1.875\cdot\sqrt{\pi}\\ &=& 1.875\cdot 1.77245385091\\ &=& 3.32335097045\\ \mathbf{2.5!} & \mathbf{=} & \mathbf{3.32335097045} \end{array}\)
What's 2.5! ? The answer is: B
A 3.32038
B 3.32335
What's 0 ÷ 0 ? The answer is: B. not "indefinite", but "undefined"
A ∞
B indefinite
What's 0^0 ? The answer is: A
A 1
B indefinite
+26367 What's 2.5! ?
\(\begin{array}{rcll} 2.5! &=& \Gamma(3.5) \\ &=& \Gamma(2.5+1) \\ &=& 2.5\cdot\Gamma(2.5) \\ &=& 2.5\cdot\Gamma(1.5+1) \\ &=& 2.5\cdot 1.5\cdot\Gamma(1.5) \\ &=& 2.5\cdot 1.5\cdot\Gamma(0.5+1) \\ &=& 2.5\cdot 1.5\cdot 0.5\cdot\Gamma(0.5) \qquad \Gamma(0.5) = \sqrt{\pi}\\ &=& 2.5\cdot 1.5\cdot 0.5\cdot\sqrt{\pi}\\\\ &=& 1.875\cdot\sqrt{\pi}\\ &=& 1.875\cdot 1.77245385091\\ &=& 3.32335097045\\ \mathbf{2.5!} & \mathbf{=} & \mathbf{3.32335097045} \end{array}\)
