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 Post subject: limit
PostPosted: Thu, 17 May 2012 18:13:54 UTC 
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lim x----0 \frac{(1+x)^\frac{1}{x}-e-e{x}}{x^2}

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 Post subject: Re: limit
PostPosted: Thu, 17 May 2012 18:55:10 UTC 
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mun wrote:
lim x----0 \frac{(1+x)^\frac{1}{x}-e+e\frac{x}{2}}{x^2}

question edited

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 Post subject: Re: limit
PostPosted: Thu, 17 May 2012 20:49:52 UTC 
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mun wrote:
mun wrote:
lim x----0 \frac{(1+x)^\frac{1}{x}-e+e\frac{x}{2}}{x^2}

question edited


I have to leave just now, but give L'Hôpital's rule a crack.

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 Post subject: Re: limit
PostPosted: Thu, 17 May 2012 21:44:31 UTC 
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mun wrote:
mun wrote:
lim x----0 \frac{(1+x)^\frac{1}{x}-e+e\frac{x}{2}}{x^2}

question edited


I'm pretty sure I have seen and answered a similar question before... indeed, it is exactly the same question in this thread.

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\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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