diff options
Diffstat (limited to 'fuvr1/n3.lyx')
| -rw-r--r-- | fuvr1/n3.lyx | 36 |
1 files changed, 18 insertions, 18 deletions
diff --git a/fuvr1/n3.lyx b/fuvr1/n3.lyx index e8b4534..ad71d13 100644 --- a/fuvr1/n3.lyx +++ b/fuvr1/n3.lyx @@ -108,7 +108,7 @@ Una función es una terna recta real ampliada \series default al conjunto -\begin_inset Formula $\overline{\mathbb{R}}:=\mathbb{R}\cup\{+\infty,-\infty\}$ +\begin_inset Formula $\overline{\mathbb{R}}\coloneqq \mathbb{R}\cup\{+\infty,-\infty\}$ \end_inset . @@ -363,7 +363,7 @@ status open \end_inset Sea -\begin_inset Formula $L:=\lim_{x\rightarrow c}f(x)$ +\begin_inset Formula $L\coloneqq \lim_{x\rightarrow c}f(x)$ \end_inset . @@ -463,7 +463,7 @@ Fijado \end_inset es de Cauchy y por tanto convergente, por lo que existe -\begin_inset Formula $L:=\lim_{n}f(x_{n})$ +\begin_inset Formula $L\coloneqq \lim_{n}f(x_{n})$ \end_inset y solo queda probar que @@ -488,7 +488,7 @@ Fijado \end_inset y -\begin_inset Formula $L^{\prime}:=\lim_{n}f(x_{n}^{\prime})$ +\begin_inset Formula $L^{\prime}\coloneqq \lim_{n}f(x_{n}^{\prime})$ \end_inset se tendría @@ -674,7 +674,7 @@ status open \begin_layout Plain Layout Si fuera -\begin_inset Formula $L:=\lim_{x\rightarrow0}\sin\frac{1}{x}$ +\begin_inset Formula $L\coloneqq \lim_{x\rightarrow0}\sin\frac{1}{x}$ \end_inset , se tendría que para toda @@ -902,7 +902,7 @@ límite por la derecha \end_inset a -\begin_inset Formula $f(c^{+})=\lim_{x\rightarrow c^{+}}f(x):=\lim_{x\rightarrow c}g(x)$ +\begin_inset Formula $f(c^{+})=\lim_{x\rightarrow c^{+}}f(x)\coloneqq \lim_{x\rightarrow c}g(x)$ \end_inset con @@ -926,7 +926,7 @@ límite por la izquierda \end_inset a -\begin_inset Formula $f(c^{-})=\lim_{x\rightarrow c^{-}}f(x):=\lim_{x\rightarrow c}g(x)$ +\begin_inset Formula $f(c^{-})=\lim_{x\rightarrow c^{-}}f(x)\coloneqq \lim_{x\rightarrow c}g(x)$ \end_inset con @@ -1431,7 +1431,7 @@ Existen \end_inset Si -\begin_inset Formula $\alpha:=\sup\{f(x)\mid x\in[a,b]\}$ +\begin_inset Formula $\alpha\coloneqq \sup\{f(x)\mid x\in[a,b]\}$ \end_inset , existe @@ -1506,15 +1506,15 @@ Demostración: \end_inset y sean -\begin_inset Formula $a_{0}:=a$ +\begin_inset Formula $a_{0}\coloneqq a$ \end_inset , -\begin_inset Formula $b_{0}:=b$ +\begin_inset Formula $b_{0}\coloneqq b$ \end_inset y -\begin_inset Formula $m:=\frac{a+b}{2}$ +\begin_inset Formula $m\coloneqq \frac{a+b}{2}$ \end_inset . @@ -1528,11 +1528,11 @@ Demostración: \end_inset , llamamos -\begin_inset Formula $a_{1}:=a_{0}$ +\begin_inset Formula $a_{1}\coloneqq a_{0}$ \end_inset y -\begin_inset Formula $b_{1}:=m$ +\begin_inset Formula $b_{1}\coloneqq m$ \end_inset , y si @@ -1540,11 +1540,11 @@ Demostración: \end_inset entonces -\begin_inset Formula $a_{1}:=m$ +\begin_inset Formula $a_{1}\coloneqq m$ \end_inset y -\begin_inset Formula $b_{1}:=b_{0}$ +\begin_inset Formula $b_{1}\coloneqq b_{0}$ \end_inset . @@ -1922,7 +1922,7 @@ Al ser \end_inset estrictamente monótona es inyectiva, y al ser -\begin_inset Formula $J:=f(I)$ +\begin_inset Formula $J\coloneqq f(I)$ \end_inset un intervalo, existe la inversa @@ -1969,7 +1969,7 @@ Al ser \end_inset estrictamente creciente, -\begin_inset Formula $d:=f(c)\in(f(c-\varepsilon^{\prime}),f(c+\varepsilon^{\prime}))=f((c-\varepsilon^{\prime},c+\varepsilon^{\prime}))$ +\begin_inset Formula $d\coloneqq f(c)\in(f(c-\varepsilon^{\prime}),f(c+\varepsilon^{\prime}))=f((c-\varepsilon^{\prime},c+\varepsilon^{\prime}))$ \end_inset , por lo que existe @@ -2002,7 +2002,7 @@ Al ser \end_inset y -\begin_inset Formula $c:=f^{-1}(d)$ +\begin_inset Formula $c\coloneqq f^{-1}(d)$ \end_inset lo es por tanto de |
