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student:mathematics:limits [2018/08/26 14:28] – bernstdh | student:mathematics:limits [2024/01/24 13:36] (current) – bernstdh | ||
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- | + | ===== Limits ===== | |
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- | ===== Mathematical Foundations: | + | |
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If you don't understand, an example should clear things right up. What happens to the fraction \(1/n\) as \(n\) gets larger and larger? | If you don't understand, an example should clear things right up. What happens to the fraction \(1/n\) as \(n\) gets larger and larger? | ||
- | Congratulations! | + | Congratulations! |
| | | | ||
- | which says that the limit of \(1/n\) as \(n\) goes to infinity is zero. | + | which says that the limit of \(1/n\) as \(n\) goes to infinity |
So, how do you talk about situations where some number is getting really large or really small? | So, how do you talk about situations where some number is getting really large or really small? | ||
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- Given two functions of \(x\), \(f_{1}\) and \(f_{2}\), with finite limits, \(L_{1}\) and \(L_{2}\) it follows that \(lim_{x \rightarrow N}(f_{1} + f_{2}) = L_{1} + L_{2}\) | - Given two functions of \(x\), \(f_{1}\) and \(f_{2}\), with finite limits, \(L_{1}\) and \(L_{2}\) it follows that \(lim_{x \rightarrow N}(f_{1} + f_{2}) = L_{1} + L_{2}\) | ||
- Given two functions of \(x\), \(f_{1}\) and \(f_{2}\), with finite limits, \(L_{1}\) and \(L_{2}\) it follows that then \(lim_{x \rightarrow N}(f_{1} f_{2}) = L_{1} L_{2}\) | - Given two functions of \(x\), \(f_{1}\) and \(f_{2}\), with finite limits, \(L_{1}\) and \(L_{2}\) it follows that then \(lim_{x \rightarrow N}(f_{1} f_{2}) = L_{1} L_{2}\) | ||
- | - (L' | + | - (L' |
- | \(f_{1}\) and \(f_{2}\), with infinite limits and derivatives \(f_{1}\prime\) and \(f_{2}\prime\), | + |