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Glossary
Calculus
When numerically evaluating more complex expressions some care is needed, as with all numerical computations, because severe cancelation can result in the numerial accuracy of a computation sometimes being unrelated to the mi,ber of desomal places, except that increasing their number normally improves numerical accuracy.
We calculate the difference of two identical numbers \( \cos \left( 2\,1o^i * \pi + y\right) - \cos (y) \) for y = 2.27. For this particular case, we use 4 decimal places and then repeat calculations with 8 decimal places.
| i | x | difference: cos(2π 10i + 2.27) - cos(2.27) | ||
|---|---|---|---|---|
| i= 1, | x= 65.1019 | difference= 4.996×10-15 | ||
| i= 2, | x= 630.589 | difference= 1.09912×10-14 | ||
| i= 3, | x= 6286.00 | difference= 1.57985×10-13 | ||
| i= 4, | x= 62834.1 | difference= 3.19367× 10-12 | ||
| i= 5, | x= 628321.0 | ddifference= 3.77282× 10-11 | ||
| i= 6, | x= 6.83781× 106 | difference= 6.83781× 10-10 | ||
| i= 7, | x= 6.28319× 107 | difference= -3.36937× 10-9 |
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