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student:mathematics:limits [2018/08/30 13:21] – bernstdhstudent:mathematics:limits [2024/01/24 13:34] – bernstdh
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 ===== Limits ===== ===== Limits =====
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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'Hopital's Rule) Given two differentiable functions of \(x\),  +  - (L'Hopital's Rule) Given two differentiable functions of \(x\), \(f_{1}\) and  \(f_{2}\), with infinite limits and derivatives \(f_{1}^{\prime}\) and \(f_{2}^{\prime}\), it follows that \(lim_{x \rightarrow \infty}(\frac{f_{1}}{f_{2}}) =  lim_{x \rightarrow \infty}(\frac{f_{1}^{\prime}}{f_{2}^{\prime}})\). 
-\(f_{1}\) and  \(f_{2}\), with infinite limits and derivatives \(f_{1}^{\prime}\) and \(f_{2}^{\prime}\), it follows that \(lim_{x \rightarrow \infty}(\frac{f_{1}}{f_{2}}) =  lim_{x \rightarrow \infty}(\frac{f_{1}^{\prime}}{f_{2}^{\prime}})\). +