diff options
Diffstat (limited to 'fuvr2/n2.lyx')
| -rw-r--r-- | fuvr2/n2.lyx | 32 |
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 |