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--- student:mathematics:limits [2018/08/30 13:21] – bernstdh
+++ student:mathematics:limits [2024/01/24 13:34] – bernstdh
@@ Line 1: / Line 1: @@
 ===== Limits =====
@@ Line 59: / Line 58: @@
   - 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  $lim_{x \rightarrow N}(f_{1} f_{2}) = L_{1} L_{2}$
-  - (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  $lim_{x \rightarrow \infty}(\frac{f_{1}}{f_{2}}) =  lim_{x \rightarrow \infty}(\frac{f_{1}^{\prime}}{f_{2}^{\prime}})$ .

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