Mister Exam

## You entered:

((3*x^2-y^2+36*x+107)*(x^2-y^2+5*x+6)-(2*x+5)*(x^3-3*x*y^2+18*x^2-18*y^2+107*x+210))/((x^2-y^2+5*x+6)^2+4*x^2*y^2+25*y^2+20*x*y^2)=0

# Plot ((3*x^2-y^2+36*x+107)*(x^2-y^2+5*x+6)-(2*x+5)*(x^3-3*x*y^2+18*x^2-18*y^2+107*x+210))/((x^2-y^2+5*x+6)^2+4*x^2*y^2+25*y^2+20*x*y^2)=0

from to
from to
from to
v

#### Quality:

(Number of points on the axis)

### The solution

You have entered [src]
/   2    2             \ / 2    2          \             / 3        2       2       2              \
\3*x  - y  + 36*x + 107/*\x  - y  + 5*x + 6/ - (2*x + 5)*\x  - 3*x*y  + 18*x  - 18*y  + 107*x + 210/
---------------------------------------------------------------------------------------------------- = 0
2
/ 2    2          \       2  2       2         2
\x  - y  + 5*x + 6/  + 4*x *y  + 25*y  + 20*x*y                               
$$\frac{- \left(2 x + 5\right) \left(\left(107 x + \left(- 18 y^{2} + \left(18 x^{2} + \left(x^{3} - 3 x y^{2}\right)\right)\right)\right) + 210\right) + \left(\left(5 x + \left(x^{2} - y^{2}\right)\right) + 6\right) \left(\left(36 x + \left(3 x^{2} - y^{2}\right)\right) + 107\right)}{20 x y^{2} + \left(25 y^{2} + \left(4 x^{2} y^{2} + \left(\left(5 x + \left(x^{2} - y^{2}\right)\right) + 6\right)^{2}\right)\right)} = 0$$
The graph of the function
The graph

### Examples of implicit functions

The above examples also contain:

• the modulus or absolute value: absolute(x) or |x|
• square roots sqrt(x),
cubic roots cbrt(x)
• trigonometric functions:
sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
• exponential functions and exponents exp(x)
• inverse trigonometric functions:
arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
• natural logarithms ln(x),
decimal logarithms log(x)
• hyperbolic functions:
hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
• inverse hyperbolic functions:
hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
• other trigonometry and hyperbolic functions:
secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
• rounding functions:
round down floor(x), round up ceiling(x)
• the sign of a number:
sign(x)
• for probability theory:
the error function erf(x) (integral of probability), Laplace function laplace(x)
• Factorial of x:
x! or factorial(x)
• Gamma function gamma(x)
• Lambert's function LambertW(x)
• Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

#### The insertion rules

The following operations can be performed

2*x
- multiplication
3/x
- division
x^2
- squaring
x^3
- cubing
x^5
- raising to the power
x + 7
x - 6
- subtraction
Real numbers
insert as 7.5, no 7,5

#### Constants

pi
- number Pi
e
- the base of natural logarithm
i
- complex number
oo
- symbol of infinity