Y=x+1

## Y=x+1

Input
y = x + 1
Geometric figure
line
Alternate form
-x + y – 1 = 0
Root
x = -1
Derivative
(d)/(dx)(x + 1) = 1
Y = x^3

## Y = x^3

Input
y = x^3
Alternate form
y – x^3 = 0
Root
x = 0
Derivative
(d)/(dx)(x^3) = 3 x^2
Y=absolute value of x

## Y=absolute value of x

Input
y = abs(x)
Alternate form assuming x and y are positive
x = y
Alternate form assuming x and y are real
y = sqrt(x^2)
Root
x = 0
Derivative
(d)/(dx)(abs(x)) = x/(abs(x))
Global minimum
min{abs(x)} = 0 at x = 0
X^0

Input
x^0
Result
1 (for x!=0)
Y^2=x

## Y^2=x

Input
y^2 = x
Geometric figure
parabola
Alternate form
y^2 – x = 0
Integer solution
x = n^2, y = -n, n element Z
Global minimum
min{y^2} = 0 at y = 0
X^-2/3

## X^-2/3

Input
1/(x^2×3)
Result
1/(3 x^2)
Roots
(no roots exist)
Derivative
d/dx(1/(x^2×3)) = -2/(3 x^3)
Indefinite integral
integral 1/(3 x^2) dx = -1/(3 x) + constant
Limit
lim_(x-> ± infinity) 1/(3 x^2) = 0
3/4 + 1/2

## 3/4 + 1/2

Input
3/4 + 1/2
Exact result
5/4
Decimal form
1.25
Mixed fraction
1 1/4
Continued fraction
[1; 4]
Egyptian fraction expansion
1 + 1/4
2x^2

## 2x^2

Input
2 x^2
Geometric figure
parabola
Root
x = 0
Polynomial discriminant
Delta = 0
Derivative
d/dx(2 x^2) = 4 x
Indefinite integral
integral 2 x^2 dx = (2 x^3)/3 + constant
Global minimum
min{2 x^2} = 0 at x = 0
1/3 x 1/3

## 1/3 x 1/3

Input
1/3×1/3
Exact result
1/9
Decimal approximation
0.111111111111111111111111111111111111111111111111111111111…
Repeating decimal
0.1^_ (period 1)
Continued fraction
[0; 9]
1/2 + 2/3

## 1/2 + 2/3

Input
1/2 + 2/3
Exact result
7/6
Decimal approximation
1.166666666666666666666666666666666666666666666666666666666…
Repeating decimal
1.16^_ (period 1)
Mixed fraction
1 1/6
Continued fraction
[1; 6]
Egyptian fraction expansion
1 + 1/6