Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
Piecewise((0,k=0),(-cos((k*pi)*x)/(pi*k),True))/l
¿Cómo vas a descomponer esta Piecewise((0,k=0),(-cos((k*pi)*x)/(pi*k),True))/l expresión en fracciones?
Solución
Ha introducido
[src]
/ 0 for k = 0
|
<-cos(pi*k*x)
|------------- otherwise
\ pi*k
-------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\cos{\left(\pi k x \right)}}{\pi k} & \text{otherwise} \end{cases}}{l}$$
Piecewise((0, k = 0), (-cos(pi*k*x)/(pi*k), True))/l
Simplificación general
[src]
/ 0 for k = 0 | <-cos(pi*k*x) |------------- otherwise \ pi*k*l
$$\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\cos{\left(\pi k x \right)}}{\pi k l} & \text{otherwise} \end{cases}$$
Piecewise((0, k = 0), (-cos(pi*k*x)/(pi*k*l), True))
Respuesta numérica
[src]
Piecewise((0, k = 0), (-0.318309886183791*cos(pi*k*x)/k, True))/l
Piecewise((0, k = 0), (-0.318309886183791*cos(pi*k*x)/k, True))/l
Potencias
[src]
/ 0 for k = 0
|
| / pi*I*k*x -pi*I*k*x\
| |e e |
<-|--------- + ----------|
| \ 2 2 /
|-------------------------- otherwise
| pi*k
\
--------------------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\frac{e^{i \pi k x}}{2} + \frac{e^{- i \pi k x}}{2}}{\pi k} & \text{otherwise} \end{cases}}{l}$$
Piecewise((0, k = 0), (-(exp(pi*i*k*x)/2 + exp(-pi*i*k*x)/2)/(pi*k), True))/l
Parte trigonométrica
[src]
/ 0 for k = 0
|
| / 2/pi*k*x\\
| -|1 - tan |------||
< \ \ 2 //
|----------------------- otherwise
| / 2/pi*k*x\\
|pi*k*|1 + tan |------||
\ \ \ 2 //
-----------------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{1 - \tan^{2}{\left(\frac{\pi k x}{2} \right)}}{\pi k \left(\tan^{2}{\left(\frac{\pi k x}{2} \right)} + 1\right)} & \text{otherwise} \end{cases}}{l}$$
/ 0 for k = 0
|
| / 2/pi*k*x\\
| -|-1 + cot |------||
< \ \ 2 //
|----------------------- otherwise
| / 2/pi*k*x\\
|pi*k*|1 + cot |------||
\ \ \ 2 //
-----------------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\cot^{2}{\left(\frac{\pi k x}{2} \right)} - 1}{\pi k \left(\cot^{2}{\left(\frac{\pi k x}{2} \right)} + 1\right)} & \text{otherwise} \end{cases}}{l}$$
/ 0 for k = 0
|
< -1
|---------------- otherwise
\pi*k*sec(pi*k*x)
----------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{1}{\pi k \sec{\left(\pi k x \right)}} & \text{otherwise} \end{cases}}{l}$$
/ 0 for k = 0
|
| /pi \
<-sin|-- + pi*k*x|
| \2 /
|------------------ otherwise
\ pi*k
------------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\sin{\left(\pi k x + \frac{\pi}{2} \right)}}{\pi k} & \text{otherwise} \end{cases}}{l}$$
/ 0 for k = 0
|
| -1
<--------------------- otherwise
| /pi \
|pi*k*csc|-- - pi*k*x|
\ \2 /
---------------------------------
l
$$\frac{\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{1}{\pi k \csc{\left(- \pi k x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}}{l}$$
Piecewise((0, k = 0), (-1/(pi*k*csc(pi/2 - pi*k*x)), True))/l