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authorJuan Marin Noguera <juan@mnpi.eu>2022-12-04 22:49:17 +0100
committerJuan Marin Noguera <juan@mnpi.eu>2022-12-04 22:49:17 +0100
commitc34b47089a133e58032fe4ea52f61efacaf5f548 (patch)
tree4242772e26a9e7b6f7e02b1d1e00dfbe68981345 /fuvr1/n3.lyx
parent214b20d1614b09cd5c18e111df0f0d392af2e721 (diff)
Oops
Diffstat (limited to 'fuvr1/n3.lyx')
-rw-r--r--fuvr1/n3.lyx36
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