🧹 More minor cleanups#8
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Jan 15, 2024
| - _What happens the range of $\beta$ values is too small? - try several small ranges_ | ||
| - _What happens if are only a few values of $\beta$ over a large range?_ | ||
| - _Does the optimal value $\beta^_$ stay the same or similar when any of the changes in this investigation are made?\* | ||
| - _Does the optimal value {math}`\beta^*` stay the same or similar when any of the changes in this investigation are made?_ |
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This is the only content change that I didn't catch in my formatter - changing unclosed "italics" across math. Putting then in a fence protects that class of errors.
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| When $\beta → 0$ we minimize the time irrespective of the fuel consumption. The gas peddle is on the floor. When $\beta → \infin$ the driver wants to use the absolute minimum amount of fuel so the gas peddle is barely engaged. This is displayed in {numref}`Figure %s <d31AdH08dO30KTmaxlYO>` where both T and F are plotted as a function of $\beta$. It is customary have the $\beta$ axis extend from a high value $\beta_H$ to a low value $\beta_L$ and this is indicated in the first two plots. A plot of $T~\text{vs}~F$ is shown in the third plot of {numref}`Figure %s <d31AdH08dO30KTmaxlYO>`. This is a monotonic curve and each point on the curve corresponds to a single $\beta$. | ||
| When $\beta → 0$ we minimize the time irrespective of the fuel consumption. The gas peddle is on the floor. When $\beta → \infty$ the driver wants to use the absolute minimum amount of fuel so the gas peddle is barely engaged. This is displayed in {numref}`Figure %s <d31AdH08dO30KTmaxlYO>` where both T and F are plotted as a function of $\beta$. It is customary have the $\beta$ axis extend from a high value $\beta_H$ to a low value $\beta_L$ and this is indicated in the first two plots. A plot of $T~\text{vs}~F$ is shown in the third plot of {numref}`Figure %s <d31AdH08dO30KTmaxlYO>`. This is a monotonic curve and each point on the curve corresponds to a single $\beta$. |
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Apparently mathjax is fine with this spelling of infinity, latex is not.
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Some minor non-content related changes.