In my previous post I looked at how to integrate a function using the Feynman technique. The function was:
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Figure 1 |
What would be good is if there was a way to convert this automatically to LaTeX, a sort of LaTeX recognition rather than text recognition. Well, it turns out that there is. I used a program called MathPix Snipping Tool and the entire page was converted instantly to LaTeX with only two minor errors. Even equal signs were aligned. This is a remarkable time saver.
Here is another try. Figures 2 and 3 shows the photographs. Figure 3 worked fine but Figure 2 gave me no end of trouble. It's important that the confidence level shows at least some red (which Figure 3 did and Figure 2 didn't). A good photograph is of course essential. The program makes multiple attempts which can then be trialed.
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Figure 2 |
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Figure 3 |
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Figure 4 |
The next example, another application of Wallis's formula, was proposed in 1957 by J. Barlaz of Rutgers University, New Brunswick, New Jersey. The solution is based on the one given the following year by
Example 3.2 Evaluate the Cesáro first order mean for the series Solution Let . Then, by Wallis's formula, Thus the Cesáro first order mean is given by
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