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student:mathematics:limits [2018/08/26 14:27] – bernstdh | student:mathematics:limits [2018/08/30 13:21] – bernstdh | ||
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- | ===== Mathematical Foundations: | + | ===== Limits ===== |
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Congratulations! | Congratulations! | ||
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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 is zero. | ||
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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 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 \(f_{2}\prime\), | + | \(f_{1}\) and \(f_{2}\), with infinite limits and derivatives \(f_{1}^{\prime}\) and \(f_{2}^{\prime}\), it follows that \(lim_{x \rightarrow \infty}(\frac{f_{1}}{f_{2}}) = lim_{x \rightarrow \infty}(\frac{f_{1}^{\prime}}{f_{2}^{\prime}})\). |