Metallic MOS: Difference between revisions
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=== As a bizarro average === | === As a bizarro average === | ||
We can think of a mediant like a bizarro average of two ratios: however we may choose to weight one, it will always lie somewhere between the two ratios. That is why we can call these two ratios its bounds. This fact is easy enough to intuit: as the weight tends toward zero, | We can think of a mediant like a bizarro average of two ratios: however we may choose to weight one, it will always lie somewhere between the two ratios. That is why we can call these two ratios its bounds. This fact is easy enough to intuit: as the weight tends toward zero, the effects of <span><math>a_1</math></span> and <span><math>a_2</math></span> drops off to nothing, and as it tends toward infinity, their effects begin to utterly overwhelm <span><math>b_1</math></span> and <span><math>b_2</math></span>. | ||
<math>\ | <math> | ||
\lim_{w\to 0} \frac{a_1w + b_1}{a_2w + b_2} = \frac{ | \begin{align} | ||
\lim_{w\to \infty} \frac{a_1w + b_1}{a_2w + b_2} = \frac{ | \lim_{w\to 0} \frac{a_1w + b_1}{a_2w + b_2} &= \frac{b_1}{b_2} \\ | ||
\lim_{w\to \infty} \frac{a_1w + b_1}{a_2w + b_2} &= \frac{a_1}{a_2} | |||
\end{align} | |||
</math> | </math> | ||