Mister Exam
Other calculators
- Derivative of a implicit defined function
- Curve tracing functions Step by Step
- Surface Plot
- Canonical form of a curve
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How to use it?
- Plot:
- y-(|x|)=(1/2)
-
y=1.6((4x/y+6)(x/y+1)/(4x/y+1))^(1/2)
-
x^2/4+y^2/9=1
-
x^2/36-y^2=1
- Canonical form:
- y^2+z^2-3z=0
- -x^2+2y^2-2xy-2x-2y+2=0
- 3x^2+y^2-12x-2y+4=0
- (x^2)/6-(y^2)/4-(z^2)/1=0
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Identical expressions
- y= one . six ((4x/y+ six)(x/y+ one)/(4x/y+ one))^(one / two)
- y equally 1.6((4x divide by y plus 6)(x divide by y plus 1) divide by (4x divide by y plus 1)) to the power of (1 divide by 2)
- y equally one . six ((4x divide by y plus six)(x divide by y plus one) divide by (4x divide by y plus one)) to the power of (one divide by two)
- y=1.6((4x/y+6)(x/y+1)/(4x/y+1))(1/2)
- y=1.64x/y+6x/y+1/4x/y+11/2
- y=1.64x/y+6x/y+1/4x/y+1^1/2
- y=1.6((4x divide by y+6)(x divide by y+1) divide by (4x divide by y+1))^(1 divide by 2)
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Similar expressions
- y=1.6((4x/y-6)(x/y+1)/(4x/y+1))^(1/2)
- y=1.6((4x/y+6)(x/y+1)/(4x/y-1))^(1/2)
- y=1.6((4x/y+6)(x/y-1)/(4x/y+1))^(1/2)
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What you mean?
- y = 4841369599423283*(4*x*x/(((4*x/(y + 1)))*(y + 1)*(y + 6)))^(13/2)/281474976710656
- y = 4841369599423283*(4*x*x/((y + 1)*(y + 6)*(4*x/y + 1)))^(13/2)/281474976710656
- y = 4841369599423283*(4*x*x/(((4*x/(y + 1)))*(y + 1)*(y + 6)))^(13/2)/281474976710656
- y = 4841369599423283*(4*x*x/((y + 1)*(y + 6)*(4*x/y + 1)))^(13/2)/281474976710656
- y = 4841369599423283*(4*x*(x/y + 1)/(((4*x/(y + 1)))*(y + 6)))^(13/2)/281474976710656
- y = 4841369599423283*(4*x*(x/y + 1)/((y + 6)*(4*x/y + 1)))^(13/2)/281474976710656
- y = 4841369599423283*(4*x*x/((y + 1)*(y + 6)*(4*x/y + 1)))^(13/2)/281474976710656
You entered:
y=1.6((4x/y+6)(x/y+1)/(4x/y+1))^(1/2)
What you mean?
Plot y=1.6((4x/y+6)(x/y+1)/(4x/y+1))^(1/2)
The solution
You have entered
[src]
___________________
/ /4*x \ /x \
/ |--- + 6|*|- + 1|
/ \ y / \y /
8* / -----------------
/ 4*x
/ --- + 1
\/ y
y = -----------------------------
5
$$y = \frac{8 \sqrt{\frac{\left(\frac{x}{y} + 1\right) \left(\frac{4 x}{y} + 6\right)}{\frac{4 x}{y} + 1}}}{5}$$
The graph of the function
The graph
Examples of implicit functions
- Trigonometric functions
x^2*sin(y) + x*y - 1 = 0
- Power functions
x^2 + x*y^2 = 1
- Exponential functions
x^y = y^x
- In the form of infinity
(x^2 + y^2)^2 - 7*(x^2 - y^2)
- A galaxy
arctg(x/y) = x*y
- Curved square
x^4 + y^4 = x^2 + y^2
- Surface defined by an implicit function
x^4*y^3*z^2 + y^4*x^3*z = x^2*z^4 + y^2
- Mordell curve
y^2 = x^3 + 1
y^2 = x^3 + 5
y^2 = x^3 + 8
y^2 = x^3 + 12
- Deltoid
(x^2 + y^2)^2 + 18*(x^2 + y^2) = 8*x^3 - 24*y^2*x + 27
- Cartesian oval
(x^2 + y^2 - 2*x)^2 = x^2 + y^2
(x^2 + y^2 - 2*x)^2 = x^2 + y^2 + 1
(x^2 + y^2 - 2*x)^2 = x^2 + y^2 - 1
(x^2 + y^2 - 2*x)^2 = x^2 + y^2 + 1/20
(x^2 + y^2 - 3*x)^2 = 1/2
- Cassini oval
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (3 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (4 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) = 0
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (6 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (7 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (8 / 5)^4
- Cissoid
x*(x^2 + y^2) + 2/7*y^2 = 0
- Cissoid of Diocles
(x^2 + y^2)*x = 2*y^2 / 3
- Conchoid of de Sluze
(x - 1)*(x^2 + y^2) = x^2
- Conchoid of Dürer
2*y^2*(x^2 + y^2) - 10*y^2*(x + y) - 2*y^2 - 9*x^2 + 90*(x + y) - 144 = 0
- Trisectrix of Maclaurin
2*x*(x^2 + y^2) = (3*x^2 - y^2) / 2
- Cruciform curve
x^2*y^2 - 9*x^2 - 4*y^2 = 0
- Ampersand curve
(y^2 - x^2)*(x - 1)*(2*x - 3) = 4*(x^2 + y^2 - 2*x)
- Bean curve
x^4 + x^2*y^2 + y^4 = x*(x^2 + y^2)
- Bicuspid curve
(x^2 - 1)*(x - 1)^2 + (y^2 - 1)^2 = 0
- Bow curve
x^4 = x^2*y - y^3
- Spiric section
(x^2 + y^2 - 6)^2 = 16*(x^2 + 1)
- Crunode
y^2 - x^2*(x + 1) = 0
- Elkies trinomial curves
y^2 = x*(81*x^5 + 396*x^4 + 738*x^3 + 660*x^2 + 269*x + 48)
- Bicorn
y^2 * (1 - x^2) = (x^2 + 2*y - 1)^2
- Bifolium
(x^2 + y^2)^2 = 3*x^2*y
- Bitangents of quartic
144*(x^4 + y^4) - 225*(x^2 + y^2) + 350*x^2*y^2 + 81 = 0
- Bullet-nose curve
y^2 - 4*x^2 = x^2*y^2
- Semicubical parabola
y^2 - 4*x^3 = 0
- Serpentine curve
x^2*y + 4*y - 6*x = 0
- Folium of Descartes
x^3 + y^3 - 6*x*y = 0
- Trident curve
x*y + x^3 + x^2 + x = 1
- Tschirnhausen cubic
x^3 = 9*(x^2 - 3*y^2)
- Witch of Agnesi
y = 8 / (x^2 + 4)
- Devil's curve
y^2*(y^2 - 4) = x^2 * (x^2 - 9)
- Hippopede
(x^2 + y^2)^2 = 2*x^2 + y^2
- Kampyle of Eudoxus
x^4 = 4*(x^2 + y^2)
- Kappa curve
x^2*(x^2 + y^2) = 4*y^2
- Lemniscate of Gerono
x^4 - x^2 + y^2 = 0
- Lemniscate of Bernoulli
(x^2 + y^2)^2 = a^2*(x^2 - y^2)
- Limacon of Pascal
(x^2 + y^2 - 3*x)^2 = 4*(x^2 + y^2)
- Cardioid
(x^2 + y^2)^2 + 8*x*(x^2 + y^2) - 16*y^2 = 0
- Trisectris Pascal
4*(x^2 + y^2) = (x^2 + y^2 - 4*x)^2
- Squircle
x^4 + y^4 = 1
- Three leaf curve
(x^2 + y^2)*(y^2 + x*(x + 1)) = 4*x*y^2
- Astroid
x^(2/3) + y^(2/3) = 1
- Atriphtaloid
x^4 * (x^2 + y^2) - (2*x^2 - 3)^2 = 0
- Nephroid
(x^2 + y^2 - 4)^3 = 108*y^2
- Quadrifolium
(x^2 + y^2)^3 = 4 * (x^2 - y^2)^2
- Elliptic curve
y^2 = x^3 + 2*x + 5
- Bolza surface
y^2 = x^5 - x
- Butterfly curve
x^6 + y^6 = x^2
- Polynomial lemniscate
(x^2 + y^2)^2 = 2*(x^2 - y^2)
- Superellipse
x^(1/2) + y^(1/2) = 1
x^(3/2) + y^(3/2) = 1
- Hyperelliptic curve
y^2 = x^5 - 2*x^4 - 7*x^3 + 8*x^2
- Cochleoid
(x^2 + y^2)*atan(y/x) = 2*y
- Cycloid
x = 2*acos(1 - y/2) - sqrt(y*(2*2 - y))
- Pursuit curve
x = 1/4*(y^2 - ln(y)^2 - 1)
x = 1/3*(1/y - 1)
- Archimedean spiral
sqrt(x^2 + y^2) = 1/2 * atan(y/x) + 3
- Fermat's spiral
x/y = cot((x^2 + y^2)/4)
- Hyperbolic spiral
y/x = tan(2/sqrt(x^2 + y^2))
- Lituus
y/x = tan(2/(x^2 + y^2))
- Syntractrix
x + sqrt(1 - y^2) = ln([1 + sqrt(1 - y^2)]/y)/2
x + sqrt(1 - y^2) = 3*ln([1 + sqrt(1 - y^2)]/y)/2
- Tractrix
x = abs(ln([1 + sqrt(1 - y^2)]/y) - sqrt(1 - y^2))
- Viviani's curve
x = 2 - z^2/2
y = abs(z*sqrt(1 - z^2/4))
y = abs(sqrt(x*(2 - x)))
z = abs(sqrt(2*(2 - x)))
x - 1 = abs(sqrt(1 - y^2))
z^2 - 2 = abs(2*sqrt(1 - y^2))
- Fish curve
(2*x^2 + y^2)^2 - 2*sqrt(2)*x*(2*x^2 - 3*y^2) + 2*(y^2 - x^2) = 0
- Oblique strophoid
x^3 + x*y^2 - x^2 + y^2 = y*(x^2 + y^2 - 2*x)
- Two parallel straight lines
9x^2+12xy+4y^2-24x-16y+3=0
- Parabola
x^2-2xy+y^2-10x-6y+25=0
- Degenerate Ellipse
5x^2+4xy+y^2-6x-2y+2=0
- Ellipse
5*x^2+4*x*y+8*y^2+8*x+14*y+5=0
- Imaginary Ellipse
8063 - 250*y - 10*x + 50*x^2 + 50*y^2
- Ellipsoid
-243 - 216*z - 18*x + 4*y^2 + 25*x^2 + 36*z^2 + 16*x*y = 0
- Imaginary Ellipsoid
2*x^2+4*y^2+z^2-4*x*y-4*y-2*z+5=0
- Double Hyperboloid
x^2+y^2-z^2-2*x-2*y+2*z+2=0
- Elliptical Paraboloid
x^2+y^2-6*x+6*y-4*z+18=0
- Two Parallel Planes
x^2+4*y^2+9*z^2+4*x*y+12*y*z+6*x*z-4*x-8*y-12*z+3=0
Learn more about Implicit function
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
- - addition
- 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