Sr Examen

Otras calculadoras

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?

Expresión a simplificar:

Solución

Ha introducido [src] 
/      0        for k = 0
|                        
<-cos(pi*k*x)            
|-------------  otherwise
\     pi*k               
-------------------------
            l
{0for k=0−cos⁡(πkx)πkotherwisel\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
{0for k=0−cos⁡(πkx)πklotherwise\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
{0for k=0−eiπkx2+e−iπkx2πkotherwisel\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
{0for k=0−1−tan⁡2(πkx2)πk(tan⁡2(πkx2)+1)otherwisel\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
{0for k=0−cot⁡2(πkx2)−1πk(cot⁡2(πkx2)+1)otherwisel\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
{0for k=0−1πksec⁡(πkx)otherwisel\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
{0for k=0−sin⁡(πkx+π2)πkotherwisel\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
{0for k=0−1πkcsc⁡(−πkx+π2)otherwisel\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
    © Sr Examen – Калькулятор