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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 /fuvr2/n2.lyx
parent214b20d1614b09cd5c18e111df0f0d392af2e721 (diff)
Oops
Diffstat (limited to 'fuvr2/n2.lyx')
-rw-r--r--fuvr2/n2.lyx32
1 files changed, 16 insertions, 16 deletions
diff --git a/fuvr2/n2.lyx b/fuvr2/n2.lyx
index b0dcf59..f71fecb 100644
--- a/fuvr2/n2.lyx
+++ b/fuvr2/n2.lyx
@@ -104,11 +104,11 @@ partición
\end_inset
, escribimos
-\begin_inset Formula $M_{i}:=\sup\{f(t)\}_{t\in[t_{i-1},t_{i}]}$
+\begin_inset Formula $M_{i}\coloneqq \sup\{f(t)\}_{t\in[t_{i-1},t_{i}]}$
\end_inset
y
-\begin_inset Formula $m_{i}:=\inf\{f(t)\}_{t\in[t_{i-1},t_{i}]}$
+\begin_inset Formula $m_{i}\coloneqq \inf\{f(t)\}_{t\in[t_{i-1},t_{i}]}$
\end_inset
, y llamamos
@@ -173,7 +173,7 @@ más fina
\end_inset
, y denotamos
-\begin_inset Formula $\pi\lor\pi':=\pi\cup\pi'$
+\begin_inset Formula $\pi\lor\pi'\coloneqq \pi\cup\pi'$
\end_inset
.
@@ -263,7 +263,7 @@ de Darboux
), respectivamente, a
\begin_inset Formula
\begin{eqnarray*}
-\underline{\int_{a}^{b}}f:=\sup\{s(f,\pi)\}_{\pi\in{\cal P}([a,b])} & \text{ y } & \overline{\int_{a}^{b}}f\mid =\inf\{S(f,\pi)\}_{\pi\in{\cal P}([a,b])}
+\underline{\int_{a}^{b}}f:=\sup\{s(f,\pi)\}_{\pi\in{\cal P}([a,b])} & \text{ y } & \overline{\int_{a}^{b}}f:=\inf\{S(f,\pi)\}_{\pi\in{\cal P}([a,b])}
\end{eqnarray*}
\end_inset
@@ -306,7 +306,7 @@ integral Riemann
\end_inset
,
-\begin_inset Formula $\int_{b}^{a}f:=-\int_{a}^{b}f$
+\begin_inset Formula $\int_{b}^{a}f\coloneqq -\int_{a}^{b}f$
\end_inset
, e
@@ -375,7 +375,7 @@ Dado
.
Entonces
-\begin_inset Formula $\pi:=\pi_{1}\lor\pi_{2}$
+\begin_inset Formula $\pi\coloneqq \pi_{1}\lor\pi_{2}$
\end_inset
cumple ambas desigualdades, pues
@@ -450,7 +450,7 @@ status open
\end_inset
Sea
-\begin_inset Formula $\alpha:=\int_{a}^{b}f$
+\begin_inset Formula $\alpha\coloneqq \int_{a}^{b}f$
\end_inset
, para toda
@@ -1134,7 +1134,7 @@ medida cero
\end_inset
, donde
-\begin_inset Formula $\text{long}([a,b]):=b-a$
+\begin_inset Formula $\text{long}([a,b])\coloneqq b-a$
\end_inset
.
@@ -1211,7 +1211,7 @@ norma
\end_inset
a
-\begin_inset Formula $\Vert\pi\Vert:=\max\{t_{i}-t_{i-1}\}_{1\leq i\leq n}$
+\begin_inset Formula $\Vert\pi\Vert\coloneqq \max\{t_{i}-t_{i-1}\}_{1\leq i\leq n}$
\end_inset
.
@@ -1662,7 +1662,7 @@ Supongamos que cambian en un punto
\end_inset
, y basta probar que
-\begin_inset Formula $h:=g-f$
+\begin_inset Formula $h\coloneqq g-f$
\end_inset
es integrable.
@@ -1715,7 +1715,7 @@ integral indefinida
\end_inset
con
-\begin_inset Formula $F(x):=\int_{a}^{x}f$
+\begin_inset Formula $F(x)\coloneqq \int_{a}^{x}f$
\end_inset
.
@@ -1769,7 +1769,7 @@ TEOREMA FUNDAMENTAL DEL CÁLCULO
Demostración:
\series default
Sea
-\begin_inset Formula $M:=\sup\{|f(x)|\}_{x\in[a,b]}$
+\begin_inset Formula $M\coloneqq \sup\{|f(x)|\}_{x\in[a,b]}$
\end_inset
, por las propiedades de la integral,
@@ -2240,7 +2240,7 @@ Demostración:
\begin_layout Standard
Esto da sentido a la notación de
-\begin_inset Formula $\int_{a}^{b}f(x)dx:=\int_{a}^{b}f$
+\begin_inset Formula $\int_{a}^{b}f(x)dx\coloneqq \int_{a}^{b}f$
\end_inset
, porque entonces si
@@ -2527,7 +2527,7 @@ Funciones que contienen
\begin_layout Standard
Llamamos
-\begin_inset Formula $d:=\frac{ac-b^{2}}{a}$
+\begin_inset Formula $d\coloneqq \frac{ac-b^{2}}{a}$
\end_inset
y se tiene
@@ -3306,7 +3306,7 @@ De aquí que si
\end_inset
y no negativas con
-\begin_inset Formula $A:=\lim_{x\rightarrow b^{-}}\frac{f(t)}{g(t)}$
+\begin_inset Formula $A\coloneqq \lim_{x\rightarrow b^{-}}\frac{f(t)}{g(t)}$
\end_inset
, entonces:
@@ -3587,7 +3587,7 @@ teorema
\end_inset
tiene derivada continua, si
-\begin_inset Formula $F(x):=\int_{a}^{x}f(t)\,dt$
+\begin_inset Formula $F(x)\coloneqq \int_{a}^{x}f(t)\,dt$
\end_inset
está acotada superiormente por