Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (25+x)-10=40
-
Equation x^2+4*x-21=0
-
Equation 2^x=10
-
Equation (x+1)^2=0
- Express {x} in terms of y where:
- 11*x+3*y=-16
- -2*x+13*y=-6
- 20*x-3*y=3
- 18*x-7*y=-4
- Derivative of:
- f*(x)
- Limit of the function:
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-oo
-
Identical expressions
- f*(x)=-oo
- f multiply by (x) equally minus oo
- f(x)=-oo
- fx=-oo
-
Similar expressions
- f*(x)=+oo
f*(x)=-oo equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Expand brackets in the left part
Divide both parts of the equation by f
We get the answer: x = -oo/f
f*(x) = -oo
Expand brackets in the left part
fx = -oo
Divide both parts of the equation by f
x = -oo / (f)
We get the answer: x = -oo/f
The solution of the parametric equation
Given the equation with a parameter:
Коэффициент при x равен
$$f$$
then possible cases for f :
$$f < 0$$
$$f = 0$$
Consider all cases in more detail:
With
$$f < 0$$
the equation
$$\infty = 0$$
its solution
no solutions
With
$$f = 0$$
the equation
$$\infty = 0$$
its solution
no solutions
False
Коэффициент при x равен
$$f$$
then possible cases for f :
$$f < 0$$
$$f = 0$$
Consider all cases in more detail:
With
$$f < 0$$
the equation
$$\infty = 0$$
its solution
no solutions
With
$$f = 0$$
the equation
$$\infty = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
oo*re(f) oo*I*im(f)
x1 = - --------------- + ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$x_{1} = - \frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
x1 = -oo*re(f)/(re(f)^2 + im(f)^2) + oo*i*im(f)/(re(f)^2 + im(f)^2)
Sum and product of roots
[src]
sum
oo*re(f) oo*I*im(f)
- --------------- + ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$- \frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
oo*re(f) oo*I*im(f)
- --------------- + ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$- \frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
product
oo*re(f) oo*I*im(f)
- --------------- + ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$- \frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
oo*(-re(f) + I*im(f))
---------------------
2 2
im (f) + re (f)
$$\frac{\infty \left(- \operatorname{re}{\left(f\right)} + i \operatorname{im}{\left(f\right)}\right)}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
oo*(-re(f) + i*im(f))/(im(f)^2 + re(f)^2)