# absolute value

Quizzes and games : function

The abs function calculates online the absolute value of a number.
abs(-5) returns 5

Quizzes and games : function

### Abs, online calculus

#### Summary :

The abs function calculates online the absolute value of a number.

abs online

# Absolute value function

The absolute value of a real number is equal to that number if it is positive, the opposite of this number if it is negative. The absolute value note abs. With this notation :

• If x>=0 abs(x)=abs(x)=x
• If x<0 abs(x)=abs(x)=-x

## Calculation of the absolute value

With the absolute value calculator, the function abs can calculate the absolute value online of a number.

To calculate the absolute value of a number, just enter the number and to apply the function abs. Thus, for calculating the absolute value of the number -5, you must enter abs(-5) or directly -5, if the button abs already appears, the result 5 is returned.

## Derivative of absolute value

The derivative of the absolute value is equal to :

• 1 if x>=0,
• -1 if x<0

## Antiderivative of absolute value

The antiderivative of the absolute value is equal to abs(x).

• intabs(x)=x^2/2 if x>=0,
• intabs(x)=-x^2/2 if x<0

## Limits of absolute value

The limits of the absolute value exist at -oo and +oo:
• The absolute value function has a limit in -oo which is +oo .
• lim_(x->-oo)abs(x)=+oo
• The absolute value function has a limit in +oo which is +oo.
• lim_(x->+oo)abs(x)=+oo

## Equation with absolute value

The calculator has a solver that allows him to solve a equation with absolute value . The calculations for obtaining the results are detailed, so it will be possible to solve equations like |x|=2 or like |2*x+4|=3 or like |(x^2-1)|=1 with the steps calculations.

## Properties of the absolute value function

The absolute value function is an even function, for every real x, abs(-x)=abs(x). The consequence for the curve representative of the absolute value function is that it admits the axis of the ordinates as axis of symmetry.

#### Syntax :

abs(x), where x is a number

#### Examples :

abs(-5) returns 5

#### Derivative absolute value :

To differentiate function absolute value online, it is possible to use the derivative calculator which allows the calculation of the derivative of the absolute value function

The derivative of abs(x) is derivative(abs(x))=1

#### Antiderivative absolute value :

Antiderivative calculator allows to calculate an antiderivative of absolute value function.

An antiderivative of abs(x) is antiderivative(abs(x))=(x)^2/2

#### Limit absolute value :

The limit calculator allows the calculation of limits of the absolute value function.

The limit of abs(x) is limit(abs(x))

#### Graphic absolute value :

The graphing calculator is able to plot absolute value function in its definition interval.

#### Property of the function absolute value :

The absolute value function is an even function.
Calculate online with abs (absolute value)
• Absolute value : abs. The abs function calculates online the absolute value of a number.
• Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccos function is the inverse functions of the cosine function.
• Arcsine : arcsin. The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
• Arctangent : arctan. The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
• Hyperbolic cosine : ch. The function ch calculates online the hyperbolic cosine of a number
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• Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
• Cotangent : cotan. The cotan trigonometric function to calculate the cotan of an angle in radians, degrees or gradians.
• Hyperbolic cotangent : coth. The coth function calculates online the hyperbolic cotangent of a number.
• Exponential : exp. The function exp calculates online the exponential of a number.
• Napierian logarithm : ln. The ln calculator allows to calculate online the natural logarithm of a number.
• Logarithm : log. The log function calculates the logarithm of a number online.
• Cube root : cube_root. The cube_root function calculates online the cube root of a number.
• Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
• Hyperbolic sine : sh. The sh function allows to calculate online the hyperbolic sine of a number.
• Sine : sin. The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
• Square root : sqrt. The sqrt function allows to calculate the square root of a number in exact form.
• Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.
• Hyperbolic tangent : th. The function th allows to calculate online the hyperbolic tangent of a number.

Real functions