Piecewise-defined function

What the calculator can do?

On this page you can get various actions with a piecewise-defined function, as well as for most services - get the detailed solution.

Derivative of a piecewise
Plot a graph
Curve sketching
Defined integral
Indefined integral of similar functions
Limit of piecewises
Fourier series (In common there are piecewises for calculating a series in the examples)
Taylor series

8 - (x + 6)^2 at x <= -6
|x^2 - 6|x| + 8| at -6 < x < 5
3 at x >= 5

Here are some examples of how to set conditions:

x≠0: x is not zero
x > pi: x greater than Pi number
-pi/2 <= x <= pi/2: x less than or equal to Pi number in half, but not strictly greater than Pi in half
true: means "otherwise"

First, set the 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 following operations can be performed