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¿Cómo usar?
- La ecuación:
-
Ecuación 2x-4=8+2x
-
Ecuación x/4+x=-5
-
Ecuación 18-x^2=14
-
Ecuación e^x=1
- Expresar {x} en función de y en la ecuación:
- -1*x+4*y=-10
- -14*x-8*y=20
- 11*x-2*y=-9
- -6*x+1*y=-5
- Derivada de:
- f*(x)
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1/x
- Límite de la función:
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1/x
- Gráfico de la función y =:
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1/x
-
Expresiones idénticas
- f*(x)= uno /x
- f multiplicar por (x) es igual a 1 dividir por x
- f multiplicar por (x) es igual a uno dividir por x
- f(x)=1/x
- fx=1/x
- f*(x)=1 dividir por x
-
Expresiones semejantes
- cos(pi*x)/(x-2)=1/(x-2)
- 1/(x-4)^2-7/x-4+10=0
f*(x)=1/x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Suma y producto de raíces
[src]
suma
/ / -im(f) re(f) \\ / / -im(f) re(f) \\ / / -im(f) re(f) \\ / / -im(f) re(f) \\
_________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/|
- / ------------------ + ------------------ *cos|---------------------------------------| - I* / ------------------ + ------------------ *sin|---------------------------------------| + / ------------------ + ------------------ *cos|---------------------------------------| + I* / ------------------ + ------------------ *sin|---------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 / / 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \
\/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/
$$\left(- i \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / / -im(f) re(f) \\ / / -im(f) re(f) \\\ / / / -im(f) re(f) \\ / / -im(f) re(f) \\\ | _________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------||| | _________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------||| | / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||| | / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||| | / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/|| | / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/|| |- / ------------------ + ------------------ *cos|---------------------------------------| - I* / ------------------ + ------------------ *sin|---------------------------------------||*| / ------------------ + ------------------ *cos|---------------------------------------| + I* / ------------------ + ------------------ *sin|---------------------------------------|| | / 2 2 \ 2 / / 2 2 \ 2 /| | / 2 2 \ 2 / / 2 2 \ 2 /| | 4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ | |4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ | \ \/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/ / \\/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/ /
$$\left(- i \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
/ -im(f) re(f) \
I*atan2|---------------, ---------------|
| 2 2 2 2 |
\im (f) + re (f) im (f) + re (f)/
-e
--------------------------------------------
_________________
/ 2 2
\/ im (f) + re (f)
$$- \frac{e^{i \operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}}{\sqrt{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}}$$
-exp(i*atan2(-im(f)/(im(f)^2 + re(f)^2), re(f)/(im(f)^2 + re(f)^2)))/sqrt(im(f)^2 + re(f)^2)
Respuesta rápida
[src]
/ / -im(f) re(f) \\ / / -im(f) re(f) \\
_________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/|
x1 = - / ------------------ + ------------------ *cos|---------------------------------------| - I* / ------------------ + ------------------ *sin|---------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \
\/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/
$$x_{1} = - i \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)}$$
/ / -im(f) re(f) \\ / / -im(f) re(f) \\
_________________________________________ |atan2|---------------, ---------------|| _________________________________________ |atan2|---------------, ---------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ im (f) re (f) | \im (f) + re (f) im (f) + re (f)/| / im (f) re (f) | \im (f) + re (f) im (f) + re (f)/|
x2 = / ------------------ + ------------------ *cos|---------------------------------------| + I* / ------------------ + ------------------ *sin|---------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \
\/ \im (f) + re (f)/ \im (f) + re (f)/ \/ \im (f) + re (f)/ \im (f) + re (f)/
$$x_{2} = i \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\frac{\left(\operatorname{re}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(f\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}},\frac{\operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \right)}}{2} \right)}$$
x2 = i*(re(f)^2/(re(f)^2 + im(f)^2)^2 + im(f)^2/(re(f)^2 + im(f)^2)^2)^(1/4)*sin(atan2(-im(f)/(re(f)^2 + im(f)^2, re(f)/(re(f)^2 + im(f)^2))/2) + (re(f)^2/(re(f)^2 + im(f)^2)^2 + im(f)^2/(re(f)^2 + im(f)^2)^2)^(1/4)*cos(atan2(-im(f)/(re(f)^2 + im(f)^2), re(f)/(re(f)^2 + im(f)^2))/2))